







Seven tangent circles 
20180423 

From Domenick: How to calculate the circumscribed and inscribed circles formed by seven .019685 diameter circles arranged in a circle with all seven circles tangent to each other? Answered by Penny Nom. 





A circle inscribed in a quarter circle 
20180416 

From abhijeet: ABC is a quarter circle and a smaller circle is inscribed in it. if AB = 1cm then find the radius of smaller circle Answered by Penny Nom. 





The sides of a circle 
20180410 

From Reid: Hello,
I recently was wondering about whether or not a circle has an infinite number of sides, and I ended up searching it on your website. I saw that you guys found the question to be too ambiguous or something of that nature, and I thought about your process of reasoning involving vertices and such. I soon realized that I may have come up with the solution to the question, but I want to confirm it with you guys. Allow me to explain:
A circle, unlike any other typical 2 dimensional polygon, can sustain an infinite number of straight lines coming in contact with only one point on it. A square, for example, cannot. A square only has 4 locations that can sustain a such a line, each of those being its corners. The flat edge of a square cannot support a tangential line, because the line would either be crossing the edge of the square or coming into contact with multiple points along its edge.
This concept is consistent in every 2 dimensional polygon: pentagons sustain 5 locations for tangential lines, hexagons 6, nonagons 9, etc.
The reason a circle has an infinite number of sides is simply the fact that it must have an infinite number of "corners", assuming it can be defined as a polygon like any of the shapes I described above.
Corners can only exist assuming there is two sides coming into contact with one another.
If there is an infinite number of corners in the circle, which is apparent due to the above reasoning, there must be an infinite number of sides coming into contact with each other.
Thus, a circle is a polygon that consists of an infinite number of sides coming into contact with each other.
Please review this reasoning and let me know if it is solid.
Thank you! Answered by Penny Nom. 





A circle problem 
20180330 

From ahamed: the diameters of a circle AB and CD intersect each other at O perpendicularly. Then a chord DF is drawn. AB and DF intersect at E. DE=6cn and EF=2cm.find the area of thw circle Answered by Penny Nom. 





Distance between a chord and its arc on a circle 
20180323 

From Doug: Specifically, what is the subject distance for the Earth orbiting for 27 days. Assume the orbit of the Earth to be a circle have a 93 million mile radius. Assume the angle of arc to be (27/365) x 360 degrees. Thank you. Answered by Penny Nom. 





A circle and two chords 
20180321 

From Ella: In a circle, a 30 unit chord is 5 units closer to the center than a 20 unit chord. Find the radius. Answered by Penny Nom. 





A circle of circumference 4*pi*r 
20180319 

From Ankith: If the circumference of a circle is 4*pi*r, what is its area?
i) 4*pi*r^2
ii) 2*pi*r^2
iii)3*pi*r^2
iv) pi*r^2 Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20180315 

From Olatundun: An Equilateral Triangle Of Side 20cm Is Inscribed In A Circle.Calculate The Distance Of A Side Of The Triangle From the Centre Of The Circle. Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20170915 

From sumit: what is the area (in sq. unit) of an equilateral triangle inscribed in the circle x^2+y^24x6y23=0. Answered by Penny Nom. 





A rope formed in a semicircle 
20170829 

From Janna: How do I find the total length of a piece of rope formed in a semicircle that has a diameter of 8 inches? Answered by Penny Nom. 





Two circles 
20170813 

From Ladines: Find the equation of the circle passing through points of intersections of circles x²+y²=4y and x²+y²=2x and the center is on line y=2 Answered by Penny Nom. 





A rectangle and a circle 
20170812 

From Ramzan: a diagram shows the shape of rectangular framework with length (2x+20)cm and with (y+10)cm . The outline is made of wire . If a circle with diameter 56 cm is to be made from the wire and the area of the rectangle is 420 square centimeter ,find the possible lengths and width of the rectangle Answered by Penny Nom. 





The equation of a circle 
20170703 

From Chen: Find the center radius and equation of a circle in standard form given the following conditions:
1. Tangent to 3x+2y=0 at the point (0,0) and passing through (1,1) and (6,0) Answered by Penny Nom. 





A polygon inscribed in a circle 
20170527 

From Levan: This was the closest to what I am trying to solve.
http://mathcentral.uregina.ca/QQ/database/QQ.09.06/s/dj1.html
So in the answer linked, we figure out what is "c".
But what if we know "c" and want to find out "n" based on specific "r=1".
It might be simple math, but I have not had any relationship with math for 20 years now
but this question puzzles me for a reason. Answered by Penny Nom. 





A trapezoid inscribed in a circle 
20170517 

From Kameron: I have been given a challenge problem that states that Diameter AB is drawn in a circle if 10 inch. Chords AC and BD are drawn so that each is of length 12inch and ACDB is a trapezoid. Find the height, in inches, of the trapezoid Answered by Penny Nom. 





Forming a cone from a circle 
20170415 

From Tasha: A sector of a circle subtends an angle of 216 degrees at the centre, If this sector is used to form a cone of vertical height ,8cm, calculate the base radius of the cone Answered by Penny Nom. 





A circle inscribed in a 30690 triangle 
20170407 

From Kameron: i have been given a problem with a 306090 triangle and a circle inscribed with a radius of 2 and was told to find the perimeter of the triangle Answered by Penny Nom. 





The volume of a slab 
20170121 

From Russell: Working with a segment of a circle. The O.D. is 3.440" the length of the chord is 3.130 I need information on the volume of the largest area. I would like to know (in thousands of an inch) how tall would the largest area need to be to equal .1143 cubic inches If you need more info I can send it Thanks in advance Answered by p. 





A circle inscribed in an isosceles triangle 
20170114 

From Sal: There is a right isosceles triangle. Inscribed inside of it, is the largest possible circle.
Ho do you find the value of the radius?
I want to find out a way of only using the rules/laws of geometry, or is that not possible. Answered by Penny Nom. 





Two concentric circles 
20161221 

From shrestha: Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of space between them. Answered by Penny Nom. 





The area and radius of a circle 
20161219 

From india: How do you find the radius of a circle if only the area is given to you? Answered by Penny Nom. 





Two tangent circles 
20161127 

From mikee: find the equation of a circle tangent to the circle x2+y2=4
and with the center at (0,5) Answered by Penny Nom. 





A circle inscribed in an equilateral triangle 
20161127 

From jo: what is the radius of the inscribed circle of an equilateral triangle with altitude 12 units? Answered by Penny Nom. 





A square inside a circle inside a square 
20161113 

From Jeff: Greetings,
I came across a question from a textbook from years ago. I've been trying to solve it, but am not sure if my approach is correct.
There are 2 squares (1 inner, 1 outer) & 1 circle.
The inner square is the largest square that will fit inside the circle. It has an area of 1 unit.
The circle is the biggest that will fit in the outer square.
What is the area of the outer square? Answered by Penny Nom. 





Three circles 
20161030 

From yolani: two equal circles with centre A (1;1)and B (4;5)touch a third circle with centre P as shown in the diagram. If P ,A and B Lie on a straight line find the coordinates of P Answered by Penny Nom. 





A circle formed from bending a wire 
20161016 

From Deszaree: The same piece of a wire is bent to form a circle
calculate:
a, the radius of the circle
b, the area of the circle Answered by Penny Nom. 





The equation of a circle 
20160930 

From Trent: write the equation of circle B with center B(2,3) that passes through (1,2) Answered by Penny Nom. 





The area of a circle 
20160812 

From sandeep: if circumference of a circle is πd what is the area? Answered by Penny Nom. 





A triangle inscribed in a circle 
20160422 

From Olyana: I am struggling with this question! Help!
So, there is a circle. In the circle, there is an equilateral triangle inscribed.
Each side of the triangle is 20. There is no other info given, other than
the triangle is inscribed in the circle and the sides of the triangle are 20.
I am supposed to find the radius of the circle! Please help! Answered by Penny Nom. 





A sector of a circle 
20160421 

From mustafa: In a sector of a circle, the arc length is equal to half the perimeter of a sector.find the area of a sector in terms of r Answered by Penny Nom. 





The area of a circle and a square 
20160410 

From Richard: I cannot understand why if you have a perimeter say of 4 units as the circumference of
a circle then you reshape it into a square you lose very approximately some 20% of its
volume but the perimeter length stays the same.
Can you please explain this to me as to why the volume decreases. Answered by Penny Nom. 





A square based box and a cylinder 
20160326 

From rajpal: i m trying to calculate an area required to hold 4.4 mln cubic metres of volume.
I used square and I get below result
A box shape that has dimensions 1500 meters (1.5km) by 1500 meters (1.5km) by 2 meters depth has a volume of:
= 4,500,000 cubic meters (4.5 mln cubic meters)
but when I use a cylinder shape, i get below result
A cylindrical shape that has a radius of 850 meters and a depth of 2 meters has a volume of:
= 4,539,600 cubic meters (4.54 mln cubic meters approx)
why is it that the cylinder, though of same depth holds more volume than a square?
kindly clarify. Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20160325 

From NIHAL: A isosceles triangle is inscribed in a circle having sides 20cm,20cm,30cm. find the radius of circle Answered by Penny Nom. 





A circle and a chord 
20160310 

From Mujtaba: The distance of a chord of length 16 cm, from the centre of the circle of diameter 20 cm Answered by Penny Nom. 





Can you construct a regular 21gon? 
20160308 

From Peter: hi, i know that if i use a compass to draw a circle, i can use the same setting to mark 6 intervals along the circle circumference, how would i go about marking out 21 equally spaced points around the circumference?
if there an online calculator i can us, or some other interesting trick?
tia
peter Answered by Robert Dawson. 





A circle is inscribed in a hexagon 
20151228 

From Lalitesh: A circle is inscribed in a regular hexagon ABCDEF
Prove that AB+CD+EF=BC+DE+FA Answered by Penny Nom. 





A diameter of a circle 
20151227 

From sahil: Find the equation of diameter of circle x2 +y26x +2y8 which passes through the origin. Answered by Penny Nom. 





Drawing an arc 
20151204 

From hassan: how to draw a curve long 1m with an angle of 22.5? Answered by Penny Nom. 





A tangent line to a circle 
20150903 

From Jamie: Use the Greek method to find an equation of the tangent line to the circle
x^2+y^24x+6y+4=0 at the points (3,2square root 23. Answered by Penny Nom. 





The diameter and circumference of a circle 
20150901 

From Tracey: Hello,
I own a custom workroom, I am figuring out fabric quantities or an estimate. When
at the job site, I forgot to measure the diameter of the semi circle shape that I have to
make a cushion for!!!
If the circumference of the semi circle is 165" what would the diameter be, maybe half
this measurement????
I appreciate any help...I basically need the width from left to right to see if I can fit
the cushion on one width of fabric that is 52" wide! Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20150611 

From Casey: I have an equilateral triangle inscribed in a circle  this triangle
has been bisected to give me 2 right triangles. I know the length
of the line bisecting the equilateral triangle is 36 inches. How do
I figure out the circumference of the circle and the length of the
sides of the equilateral triangle? Answered by Penny Nom. 





A pentagon inscribed in a circle 
20150530 

From Victoria: find the area of a regular pentagon inscribed in a circle with radius 3 units Answered by Penny Nom. 





Two concentric circles 
20150528 

From Shannan: Two concentric circles have radii of 24cm and 26cm. What is the length of the chord that is tangent to the inner circle? Include a sketch Answered by Penny Nom. 





The perimeter of a quarter circle 
20150521 

From Bethany: The perimeter of a quarter circle is 3.57. What is the quarter circle's radius? Answered by Penny Nom. 





A triangle inscribed in a circle 
20150507 

From R2D2: A triangle is inscribed in a circle of radius 10. If two angles are 70 degrees and 50 degrees find the length of the side opposite the third angle? Answered by Chris Fisher. 





A circle is tangent to the yaxis 
20150506 

From Elynna: What does it mean when a circle is tangent to the yaxis?
Thanks, Answered by Penny Nom. 





Locating the center of a circle that forms an arc 
20150423 

From Ken:
Find the Cartesian coordinates of the center of an arc with the given location of the beginning and end points and radius length. Not the midpoint of the circumference but the actual point that the arc
is drawn around.
I know their are two answers depending on the direction of the arc. Unless we assume that all arcs are drawn counter clock wise.
Thanks
Ken
Answered by Harley Weston. 





Two concentric circles 
20150421 

From Juniper: Two concentric circles have radii of 4 cm and 8 cm. A segment is drawn so that it is tangent to the smaller circle and a chord of the larger circle. How long is the segment? Answered by Penny Nom. 





A circle inscribed in a square 
20150419 

From michael: A circle is drawn in a square PQRS. If the total area of the shaded portion of the square is 42 cm square, calculate the radius of the circle Answered by Penny Nom. 





The area of a circle given the circumference 
20150412 

From F: How do you find the area of a circumference of 6?
Thanks. Answered by Penny Nom. 





An 8 pointed star inscribed in a circle 
20150410 

From Kermit: How do you find the area of the star that is formed by two squares and surrounded by a circle. The only given information is that the radius of the circle is 10. Answered by Penny Nom. 





The perimeter of a quarter circle 
20150410 

From Riley: How do you find the perimeter of a quarter circle when the radius is 56? Answered by Penny Nom. 





The area of the ring between two concentric circles 
20150408 

From Conner: The area of the ring between two concentric circles is 25pi/2 square inches. The length of a chord of the larger circle tangent to the smaller circle is? Answered by Robert Dawson. 





A circle graph 
20150406 

From Davis: i don't know how to answer this question. please help!
a survey about student government shows the following results
110 like the program
120 think the program is unnecessary
210 plan on running for student government next year
if this information is put in a circle graph,what is the central angle for the students who like the program? Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20150323 

From Rachel: Triangle ABC is an isosceles triangle inscribed in circle O. If each leg of the triangle is 13cm and the altitude to the base of triangle ABC is 5cm, find the radius of the circle. Answered by Penny Nom. 





Two parallel tangents to a circle 
20150305 

From Samantha: The equation of a circle is x^2+y^2=25. Determine
the equation of the parallel tangent lines to this
circle, for which the slope is 4/3. Answered by Penny Nom. 





Two concentric circles 
20150225 

From Manasi: The area between 2 concentric circles is 6 times the smaller circle. Radius of small circle is 7 cm. Find the difference in the circumference of the bigger circle ad the smaller circle? Answered by Penny Nom. 





A circle and a chord 
20150207 

From Dakota: If the diameter of a circle is 48 cm, find the shortest distance from a chord of length 34 cm to the center of the circle Answered by Penny Nom. 





The center and radius of a circle 
20150206 

From ariana: I need to find the center and the radius of this circle. I don't know how to put 9/2
than square it into a fraction.
x^2 + 2x + y^2 +9y=5 Answered by Penny Nom. 





Two concentric circles 
20150125 

From nazneen: select the correct answer from the given four options
given are two concentric circles. radii of outer circle & inner circle are r1 & r2 respectively.
the areas of inner circle & shaded ring are equal. the radii r1 & r2 are related by?
1. r1 = r2
2. r1 = r2*square root 2
3. r1 = r2*square root 3
4. r1 = 2r2 Answered by Penny Nom. 





The perimeter of a quarter circle 
20141226 

From Maisy: This is the question that I got for a math worksheet.
The radius of a quarter circle is 5 miles. What is the quarter circle's perimeter?
Use 3.14 for pi. Answered by Penny Nom. 





A tangent to a circle 
20141222 

From azman: Find the equation of the tangent line to the circle x^2+y^2=9 at the point P (2, square root of 5). Answered by Penny Nom. 





A circle through 3 points 
20141204 

From priyanka: Find the equation of a circle passing through the origin and intercept on axes are a and b. Answered by Penny Nom. 





An irregular convex octagon 
20141113 

From james: I have an irregular convex octagon, alternating between 4 large edges, say 'a' mm long and 4 small edges, say 'b' mm long, is there a formula available so that I can work out the minimum size sit a circle with a radius of 34.25mm inside it thank you Answered by Chris Fisher. 





The area of a circle in terms of the circumference 
20141104 

From Sarah: How do you find the area of a circle if you already have the circumference?
There was one answer to this question already but it didn't make sense to
me, because they rounded up pi which you can't do so the answer is
incorrect. thanks Answered by Penny Nom. 





The region between two concentric circles 
20141027 

From Ray: two circles, concentric; Given the length of chord of outer circle that is tangent to inner circle. what are the areas of both? how to calculate? Answered by Penny Nom. 





How does pir^2 = 1/4pid^2? 
20141014 

From al: Hi I cant work out the algebra. How does pir^2 = 1/4pid^2 Thanx Answered by Penny Nom. 





Trig functions and the unit circle 
20141002 

From Jake: I was wondering what conclusions can be drawn about the trigonometric functions and how they work about the circle. Can you also please give me an explanation for it? Thank you. Answered by Penny Nom. 





Two chords in a circle 
20140913 

From Carlos: Find the length of the radius of a circle in which a
chord of length 6 units is twice as far from the
center as a chord of length 12 units Answered by Penny Nom. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





The equation of a circle 
20140814 

From jennifer: hi there My name is Jennifer and residing in Denmark. I am a student and I wrote to you because i am having trouble in finding out the equation for the circle using
(xa)^2 + (yb)^2 =3D r^2.The diameter of this circle is d=3D 44,514 cm.
I have attached a drawing of my problem..thanks Answered by Penny Nom. 





Covering a 12 inch by 12 inch square hole 
20140702 

From Patricia: I am putting in a new bathroom fan. I am wondering if a new light with a 15 inch diameter will cover the existing square hole which is 12 by 12 inches? If the existing hole is 11 1/2 by 11 1/2 inches?
Also, if the 15 inch diameter does not cover the 12 by 12 hole, what size diameter would?
Thank you. Answered by Penny Nom. 





The area of a circle of circumference 32.69 meters 
20140611 

From coco: Find the area of a circle with a circumference of 32.69 meters. Answered by Penny Nom. 





A circle a square and a rectngle 
20140512 

From mazhar: suppose the length and breadth of the rectangle are 5 cm and 10 cm respectively and M is a point along the corner of the circle. what is the radius of the circle?(diagram is given..but i didn't mention it..actually the diagram looks like a circle inscribed in a square and the right bottom corner one rectangle will be given ,it is touches to circle at a point M that I've already mentioned and the dimensions of that rectangle also I've mentioned) please help me out.. Answered by Penny Nom. 





A circle is divided into three sectors 
20140417 

From atolagbe: the area of a circle is 154cm square. it is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. calculate the perimeter of the third sector. take pi=22/7? Answered by Penny Nom. 





Two circles that touch each other externally 
20140408 

From Ameya: Two circles of radii a and b (a > b) touch each other externally. ST is a common tangent touching the circles at S and T respectively, then ST^2 is equal to Answered by Chris Fisher. 





Cutting a hexagon from a disk 
20140405 

From Paul: I am a machinist and sometimes need to make a hex from
round material.
If I know the distance of the flat sides opposite one another
of my hex, how can I calculate the size of material I need to turn
to give me the right diameter to finish the part with six sides? Answered by Penny Nom. 





A circle inscribed in a right triangle 
20140316 

From akshaya: A circle with centre O and radius r is inscribed in a right angled triangle ABC. If AB=5 cm, BC=12 cm and < B=90*, then find the value of r. Answered by Penny Nom. 





Two overlapping arcs in a square 
20140315 

From Jean: I have a square with side 4 cm. There are two overlapping arcs going from vertex to diagonal vertex. The other two vertices are the center of the arcs, which are shaded. How do I find the area of the shaded arcs? The overlapping arcs when shaded resemble a long thin football
Thank you for your help. Answered by Penny Nom and Walter Whiteley. 





A circle which is tangent to two perpendicular lines 
20140309 

From MJ: I'm a College Student taking up Bachelor of Secondary Education on Math Subject.
And I'm struggling for my research about Circles. I done solving the said topic particularly on this question:
"What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ"
But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem.
Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle.
Thanks in advance! :) Answered by Penny Nom. 





The equation of a circle 
20140307 

From Balraj: I have to draw a circle x^2+y^2 =8x . please tell me how to understand these coordinates ? please elaborate , on how to understand these types of equations. Answered by Penny Nom. 





A circle graph 
20140306 

From Caitlyn: I need to find the measure of the central angle that represents the amount of time spent on each activity.
My question includes a circle graph with the following: Sleep 31%, Other 15%, Entertainment 18%, Errands 7%,
Work 20%, and Food 9%. Answered by Penny Nom. 





A circle through three points 
20140222 

From Mohammad: Find the equation of circle passing through the origin and the points (a,b) and (b,a).
Find the length of chords that it cuts off from the axes. Answered by Chris Fisher. 





A rectangle inscribed in a circle 
20140110 

From Marian: A 16 cm by 12 cm rectangle is inscribed in a circle. Find the radius of the circle. Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20140106 

From Anonymous: An equilateral triangle with sides 6 inches is inscribed in a circle. What is the diameter of the circle? Answered by Penny Nom. 





A circle insubscribed in an isosceles trapezoid 
20131208 

From Bob: A circle is insubscribed in an isosceles trapezoid, with
parallel lengths of 8cm and 18cm.
What is the lengths of sloping edges and why? Answered by Robert Dawson. 





2 concentric circles 
20131127 

From Dimaris: The radius of the outer circle of 2 concentric circles is x. An
equilateral triangle inscribed in the outer circle also circumscribes the
inner circle. What is the radius of the inner circle in terms of x? Answered by Penny Nom. 





A string wrapped around three circles 
20131019 

From Jim: A recent puzzle ' find the length of a string around 3 touching
1 meter diameter circles ' gave this answer : the string
touches 120° (or pi/3 meters) of each circle. Then
3(1+pi/3) = 3+pi meters is the required length. I do not see how
it was determined that the string touches 120° or pi/3 meters?
Please explain . Thankyou , Jim Answered by Penny Nom. 





A square inscribed in a circle 
20131014 

From Jenn: Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you! Answered by Penny Nom. 





Four tangent circles 
20131009 

From Nilesh: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. How to find the area of the space enclosed by the four pieces?
Please let me know. Answered by Robert Dawson. 





The area of a semicircle 
20130728 

From Lucy: Find the area of the the figure described: a semicircle with arc length 3 pi. Answered by Penny Nom. 





Four circles 
20130529 

From varsha: four circular cardboard pieces each of radius 7cm are placed in such a way that each piece touches two other pieces. find the area enclosed by the four pieces. Answered by Penny Nom. 





Two overlapping circles 
20130522 

From Alexandra: There are two overlapping circles. The two nonoverlapping regions have areas A and B.
As the area of overlap changes, the values of A and B also change.
Prove that no matter how big and small the overlap is, the difference between
A and B is always the same. Answered by Penny Nom. 





A circle and a chord 
20130514 

From yashvardhan: A circle which radius 13cm. Find the length of the chord which is 5 cm away from center Answered by Penny Nom. 





A triangle and an incircle 
20130509 

From Max: On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line.
The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this. Answered by Chris Fisher. 





A circle, a chord and an arc 
20130416 

From Tim: Morning,
I was told the chord is 3000mm and the depth of chord is 300mm, I can
find the radius,(1500 squared + 300 Squared) Divided by (300 + 300)
but don't know how to calculate the length of the circle defined by the chord.
Regards
Tim
Answered by Penny Nom. 





The tangent to a circle at a point on the circle 
20130222 

From Andrew: What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (4,3) Answered by Penny Nom. 





The equation of a circle 
20130211 

From mhd: Complete the equation of the circle centered at(0,4) with radius 3 Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20130117 

From Nicole: How do you find the shaded region of a circle if an unshaded equilateral triangle in inscribed in it. The only other things I know about the problem are that the side lengths of the equilateral triangle are 14 inches. Answered by Penny Nom. 





Milling round stock to square stock 
20121217 

From Bryan: Question from Bryan:
I want to know what the smallest diameter round is that will make a 31/4" square? Is there a formula for that? I am milling round stock into square.
Thank you. Answered by Harley Weston. 





A circle inscribed in a triangle 
20121128 

From Angie: Circle O is inscribed in triangle ABC. Angle A = 50 and angle B = 60. Find arc XY in dgrees Answered by Penny Nom. 





A path around a pond 
20121116 

From bailey: hi there,
A circular pond is surrounded by a path 1 metre wide.
The area of the path is 1/4 of the area of the pond.
Find the radius of the pond.
Thanks Answered by Penny Nom. 





Two congruent circles in a rectangle 
20121020 

From Alexander: Have you ever solved a problem, in which you have a rectangle, from which you need to cut the largest two circles of equivalent diameter? I bisected a rectangle diagonally, but the circles, while tangent to two of the sides, are not tangent to eachother. Can you devise a method for two equivalent circles, that are tangent to two sides, are also to eachother?
Take for example a piece of paper, Each if the two largest circles has a diameter that is greater than the distance to the midpoint of the diagonal bisector of the rectangle. Answered by Chris Fisher. 





The degree measure of the central arc of a circle 
20121017 

From Crystal: On a circle with radius of 12 cm is an arc of length 20 cm. What is the degree measure of the central angle used to make this arc? Answered by Penny Nom. 





Two circle problems 
20121005 

From shahad: question 1
find an equation for the circle through the point (0,0) and (6,0) that a tangent to the line y=1
question 2
find an equation for the circle through the point (0,0) and (17,7) whose center lies on the line 12x5y=0 Answered by Penny Nom. 





Four tangent circles 
20121004 

From renu: inside of a circle K of radius length measure R,three circular discs A,Band C each of radius r are placed so that each touches the other two and K . express R in terms of r. in the space between K, A and B , another circular disc D is placed which just touches K, A and B. if the radius is s, show that (6+root3)s=(2+root3)r Answered by Penny Nom. 





An equilateral triangle and a regular hexagon in a circle 
20120911 

From Heidemarie: The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle. Answered by Penny Nom. 





The distance between overlapping circles 
20120726 

From Jeff: I have two circles of different size that overlap one another:
Circle #1 has an area(A) of 731,475, so I can calculate its radius as 482.6.
Circle #2 has an area(A) of 502,517, so I can calculate its radius as 400.
If I know that the area where they overlap is 179,271, how can I calculate the distance between the midpoints of these two circles? Answered by Chris Fisher. 





A regular hexagon inscribed in a circle 
20120725 

From jim: A regular hexagon with an area of 24√3 is inscribed in a circle. What is the area of the circle? Answered by Penny Nom. 





A reel of cotton thread 
20120605 

From Grace: 91 meters of cotton goes round the cotton reel. About how many times does the cotton go round the reel?
Give your answer to the nearest ten.
(The Diameter of the cylinder is 3cm) Answered by Penny Nom. 





The area of a semicircle 
20120528 

From Rebecca: how do you find the area of a semi circle and then how do you add the area of a semi circle and the area of a rectangle? Answered by Penny Nom. 





A 10 inch circle using 2x4s 
20120519 

From Ralph: I want to form a 10" circle with 4"high pieces of 2 x4's. If each 2x4 piece sit next to each other,What degree would I have to cut
each side of the 2x4's, and how many would I need to form a 10 inch circle. I know there is a formula for this out there somewhere. Answered by Harley Weston. 





A circle inscribed in a triangle inscribed in a circle 
20120426 

From Maty: How do i find the area of a triangle inscribed a circle while another smaller circle is circumscribed by the same triangle and the radius is 8. Answered by Chris Fisher. 





A common chord to two circles 
20120422 

From Nicole: What is a common chord between two circles and how is it found in the problem: Two circles intersect and have a common chord, the radii of the circles are 13 and 15, the distance between the circle's centers is 14, find the common chord. Answered by Penny Nom. 





The sarsen circle 
20120421 

From Firdous: I found the circumference but after what to do I am not getting the question is.The diameter of the sarsen circle is 33 meters,since there were originally 30 sarsen stones located on the circumference, how far apart wold the centres of the stones have been?Round to the nearest tenth of a meter. Answered by Penny Nom. 





A tangent line to a circle 
20120414 

From Novelyn: find an equation of the line tangent to a circle with equation x^2+y^2+6x8y27=0 at the point P(1,2) Answered by Penny Nom. 





A circle drawn around a equilateral triangle 
20120401 

From BIMAL: what is the diameter of a circle drawn around a equilateral triangle of size 6 cm Answered by Penny Nom. 





Two overlapping circles 
20120321 

From Monty: If you have a 3.75" radius circle overlapping a 5" radius circle with their centers 3" apart what would be the area of the nonoverlapped portion of the small circle? Answered by Penny Nom. 





Circles 
20120311 

From Deniz: Two circles are externally tangent and the lengths of their diameters are 4 and 6. Find the length of the segment joining the centers of the circles. Answered by Penny Nom. 





A circle inscribed in a quarter circle 
20120220 

From sonam: ABC is a quarter circle and a circle is inscribed in it and if AB=1cm than find radius of a small circle. Answered by Penny Nom. 





A circle and a chord 
20120211 

From Sophia: The diagram shows a circle with a chord that is 10cm long. The middle of the chord is 12cm from the centre of the circle. Calculate the radius.
Chord length is 10cm.
The distance from the centre to chord is 12 cm. Answered by Penny Nom. 





Two circles 
20120208 

From crisfe: find the point where the common cord of the circles x2+y2=25, x2+y212x6y+35=0 process there line centers. what point they intercepts? Answered by Penny Nom. 





Great circle course 
20120125 

From Hervé: On the earth, the mathematical formula giving the distance
between two points, and the initial course for a boat on the great circle
is well known.
I need to find the inverse formula, ie knowing an initial position on earth,
and the initial course of the boat, and the distance to run on the great circle,
the formula gives the final position (longitude and latitude). Answered by Robert Dawson. 





A fountain 
20120124 

From kris: A fountain has a radius of 14 meters to its outer edge. Their is an inner ring in the center of the fountain, where a statue of Sir Isaac Newton stands, that does not contain water. The inner ring has a diameter that is 6m less than the diameter of the outer ring of the fountain. What is the circumference of the inner ring? What is the area that is covered by water in the fountain? Answered by Penny Nom. 





Four pizzas 
20120123 

From kris: a pizza company wishes to put 4 medium pizzas in a box to sell as a party pack. The box they want to use the square and has dimensions of 60cm by 60cm. They need you to help them calculate the dimensions of the pizza that will fit in the box. Calculate the following: area, radius, diameter, circumference Answered by Penny Nom. 





A circle inscribed in a regular octagon 
20120116 

From Eric: I have a circle inscribed in a regular octagon. How do I determine the length of one side of the octagon if I know the radius of the circle (2.75 inches) ? Answered by p. 





The radius of a circle 
20120112 

From Janie: Find the radius of a circle knowing that a chord of 24.6 inches has a corresponding arc of 70°. Answered by Penny Nom. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





Two shapes 
20120106 

From muhammad: Question from muhammad, a student:
a boy has two pieces of wire each 99cm long .he bends them into the shapes shown below.calculate the radius of each figure,giving each answer to two decimal places.figures are one is semicircle and other on is half of the semicircle. Answered by Harley Weston. 





The circumference and area of a circle 
20111213 

From Mable: A circle that going 70mi across using 22/7 I need the area,radius, and the circumference
and how to set up the steps can you help? Answered by Penny Nom. 





Two circles 
20111204 

From Luke: Two fixed circles intersect at A and B.
P is a variable point on one circle.
PA and PB when produced meet the other circle at M and N respectively.
Prove that MN is of constant length.
Thanks!
p.s. I also sent the question with a figure via email. Answered by Chris Fisher. 





The perimeter of a quarter circle 
20111110 

From sierra: how do you figure the perimeter of a quarter circle that has a radius of 12 Answered by Penny Nom. 





The area of a circle 
20111017 

From Winney: If the diameter of a semicircle is 3 feet what is the area. Answered by Penny Nom. 





One central circle and three tangent circles 
20111016 

From Margaret: You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates? Answered by Chris Fisher. 





Two great circles 
20111006 

From Jean: "Two great circles lying in planes that are perpendicular to each
other are drawn on a wooden sphere of radius "a". Part of the sphere
is then shaved off in such a way that each cross section of the
remaining solid that is perpendicular to the common diameter of the
two great circles is a square whose vertices lie on these circles.
Find the volume of this solid."
I don't understand the geometry of the problem.
Can you please explain the problem and if possible draw a diagram for me
? Answered by Chris Fisher. 





A trapezoid inscribed in a circle 
20111002 

From Greg: A trapezoid is inscribed within a circle.
The two interior angles who share the longest side are 70 and 80.
The arc whose chord is the longest side has a length of 120.
Find the other two interior angles of the trapezoid, and the other three arc lengths. Answered by Chris Fisher. 





Decartes' circle theorem 
20110907 

From Joseph: Given 3 circles of diameters 50, 55, and 60 units,
Place them externally tangent.
What is the diameter of the outer circumscribing circle,
tangent to all 3 circles? I can attach a pdf if this description is not clear.
Not urgent, this has nothing to do with current assignments,
just wondering if I have developed the best methods? Answered by Chris Fisher. 





Three tangent circles 
20110821 

From maribie: three discs are tangent externally distances between their centers are 23cm, 15cm, and 20cm. find their radii.t Answered by Penny Nom. 





Three tangent circles 
20110819 

From hanniel: two coin are tangent to a third coin internally and are tangent to each other
externally. The distance between their centers are 14 mm, 17mm, and 5mm.
find their radii Answered by Penny Nom. 





A 3 foot circle using 1/2" cord 
20110804 

From Cindy: To make a 3 foot circle using 1/2" cord  how many lineal feet of cord
do I need? Answered by Robert Dawson. 





A point on a circle 
20110802 

From George: I know the center location (x,y) of the circle, I know the radius of the circle, I know the location (X,Y) of one point on the circle, and I know the angle (in degrees not radians) between the known point location (X,Y) and an unknown point location (let's call it (A,B) for reference). What formula(s) can I use to find out the coordinate position of (A,B)? Answered by Chris Fisher. 





A regular hexagon inscribed in a circle 
20110718 

From Courtney: If ABCDEF is a regular hexagon inscribed in a circle of
radius r, prove that the length of each side of the hexagon
equals r. Answered by Penny Nom. 





A rectangle is inscribed in a circle 
20110717 

From Alexea: A rectangle is inscribed in a circle of diameter 15in. Express the perimeter as a function of the width x. Answered by Penny Nom. 





concentric circles 
20110706 

From maribiie: two circles are concentric. the tangent to the inner circle forms a chord of 12cm in the larger circle. find the area of the "ring" between the two circles? Answered by Penny Nom. 





A circle inscribed in a triangle 
20110507 

From Aishwarya: The angles of a triangle are 50, 60, and 70 degrees, and a circle is touches the sides at A, B, C. Calculate the angles of the triangle ABC. Answered by Penny Nom. 





Three tangent circles 
20110501 

From mark: Three circles of radii 24 cm, 32 cm, and 42 cm are externally tangent to each
other (each is tangent to the other two). Draw a diagram and using the Law of
Cosines find the largest angle of the triangle formed by joining their centres. Answered by Penny Nom. 





cos(x) = 1/(square root of 2) 
20110427 

From Shelby: Find exact value of x for 1 <(or equal to) x < 2pi
a) cos(x) = 1/(square root of 2) Answered by Penny Nom. 





The length of a chord 
20110425 

From G: A 120 degree central angle intercepts a circle at the points A and B. The radius of the circle is 10 cm. Find the length of chord AB. Answered by Penny Nom. 





The degree measure of an arc in a circle 
20110408 

From Deb: How do I find the degree measure of an arc in a circle with the Length of 14 and the radius of 70? Answered by Penny Nom. 





A circle in a square in a circle in a square 
20110329 

From George: A circle within a square which is inside
a larger circle which is also within a square.
(a circle in a square inside a circle in a square)
Equation of the smaller circle is: x ^ 2 x y ^ 2 = 25.
What are the dimensions of the larger square?
Been 40 years, trying to help my son. Answered by Penny Nom. 





A family of circles 
20110301 

From steffi: Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 4x28=0 and x^2 +y^2 4x20+52=0; the member tangent to x=7. Answered by Penny Nom. 





A circle is inscribed inside an isosceles trapezoid 
20110225 

From priyam: a circle is inscribed inside an isosceles trapezoid (with parallel sides
of length 18 cm and 32 cm) touching all its four sides.
find the diameter of the circle.
thanks for help!! Answered by Penny Nom. 





The equation of a circle 
20110214 

From Cristela: find the equation and all the information in General Form and Standard Form of the Circle that will passed trough the point (2,3) (6,1) (4,3) Answered by Stephen La Rocque. 





Two tangent circles 
20110209 

From xhesika(jessica): Two circles of radius 10 are tangent to each other.A tangent is drawn
from the centre of one of the circles to the second circle.To the nearest
integer find the area of the shaded region. Answered by Penny Nom. 





A tangent to a circle 
20110206 

From debz: what is the formulae of the tangent to a circle.... our teacher gave us a lot of homework.. and she ask us to find the formulae by ourselves.. Answered by Penny Nom. 





The perimeter of a semicircle 
20110129 

From Keith: I have the perimeter of a semi circle of 37 but how do I calculate the diameter from this.
This is all the information I have. Answered by Penny Nom. 





Semicircles and the Pythagorean Theorem 
20110109 

From Jas: Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question:
****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer??
I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer! Answered by Penny Nom. 





A sector of a circle 
20110107 

From Alice: the radius of a circle is 7cm the angle of the sector is 68 how do you find the Answered by Penny Nom. 





A circle inside a square 
20101231 

From Jenn: A circle of a diameter of 2 is drawn inside a square of 4. The circle's center is at the center of the square. To the nearest tenth, what is the perimeter of the area of the square, not including the circle inside. Answered by Penny Nom. 





The perimeter of a quarter circle 
20101215 

From kim: how do you figure the perimeter of a quarter circle that has a radius of 7 inches? I would like to have the explanation of how you figure it out. Thank you Answered by Penny Nom. 





Two chords in a circle 
20101202 

From girma: one chord of a circle is 8cm long and it's distance from the center is 4cm long.what will be the length of another chord, of the same circle ,which is 2cm from the center Answered by Penny Nom. 





A sector of a circle 
20101129 

From Mel: Find the area of a sector of a circle that has a central angle of 13pi/18 and a radius of 12cm. Round answer to nearest 10th degree Answered by Penny Nom. 





The perimeter of a semicircle 
20101111 

From gayathri: the area of semicircle is 1925sq.cm find perimeter Answered by Stephen La Rocque. 





The equation of a circle 
20101020 

From Silvan: Hi, I just want to find the x,y values for the circumference of a circle...
Lets take a clock having its centre at (0,0) in a graph.
I just want to know how to find the (x,y) coordinates for the curved path or the surface of the circle..
Is there any formula to directly align the curved path or the circumference of the circle in a graph for a known radius of a circle..
I feel it will be useful for me to draw a clock in a graph... :) Answered by Penny Nom. 





Limiting Cases in Geometry 
20100922 

From Niki: Consider a rectangle inscribed in a circle with a radius or R. What are the possible perimeters for the rectangle? Answered by Stephen La Rocque. 





Find the point of contact of the circles 
20100920 

From Sandra: If the center of circle A = (1,3) and the radius of it is √20,
the center of circle B = (5,9) and the radius of it is √80.
Find the point of contact of the circles A and B. Answered by Janice Cotcher. 





The circle centered at (2,4) with radius 3 
20100918 

From lupe: Consider the circle centered at (2,4) with radius 3. Write the equation
of this circle sketch its graph, and find the exact coordinates of its intercepts.
xintercept
yintercept using the quadratic equation? Answered by Penny Nom. 





Two overlapping circles 
20100804 

From Husen: two circles of radius 5 cm intersect each other .the distance between their centers is 5root 2.find the area of the portion common to the two circles Answered by Penny Nom. 





The diameter of a circle 
20100624 

From John: Piece of wire 72cm in length bent to make semicircle and diameter.Find
length of diameter.Answer given 28cm.How is this arrived at?Looked at
circumference in various ways but failed to understand how 28 cm was
arrived at.Thanks for the help. Answered by Robert Dawson. 





The equation of a circle 
20100623 

From Michelle: Write and equation for the circle with a center, (0,0) and a diameter of 12 Answered by Penny Nom. 





3 equidistant points on a circle 
20100621 

From Brian: We have to line up 3 pins on a lifting bridle to be 120 degrees apart from each other to connect into a lifting assembly.
I know pi*d. I know straight lines connecting these points to each other will result in an equilateral triangle.
How does one find these points without using a protractor? There must be a formula (formulae) to work this out mathematically.
r = 10.5 inches
pi*d = 65.9736
3 segments( arcs) = 21.9912 which is the distance along the circumference that the points are from each other. Answered by Penny Nom. 





The area of a circle 
20100612 

From grier: please,
what is the area of a semicircle with arc length 3pi? Answered by Penny Nom. 





Four circles in a square 
20100604 

From Daniela: four circles are drawn in a square such that the circles are tangent to each other as shown. find the area of the shaded region. It the goes on to show a diagram with a square and four circles drawn in it. The length of a side of the square is 24. Please help me! Answered by Penny Nom. 





A square inscribed in a circle 
20100525 

From Middle: what is the perimeter of a square inscribed in a circle of radius 5.0 inches? Answered by Penny Nom. 





The circumference of a circle 
20100512 

From Morgan: find the circumference of a circle with radius 8.
im having trouble i just don't understand. thanks for your help i really do appricate it. Answered by Penny Nom. 





The equation of a circle 
20100504 

From crystal: find the standard form of the circle with center (2,3) and tangent to the line y=1 Answered by Penny Nom. 





The diameter of a circle 
20100430 

From Jimmy: If I have a straight line with a known length and decide to make a circle out of this know length how would I calculate what the diameter of the circle would be Answered by Penny Nom. 





A circle inscribed in a square inscribed in a circle 
20100428 

From jouniella: A square is inscribe to the first circle, then another circle is inscribe to the square. Find the ratio of the 2 circles. Answered by Penny Nom. 





The area of semi circle 
20100416 

From sagir: how to find the area of semi circle? Answered by Penny Nom. 





A tangent line to a circle 
20100415 

From Rhonda: The Greek method for finding the equation of the tangent line to a circle used the fact that at any point on a circle the line containing the reauis and the tangent line are perpendicular. Use this method to find an equation of the tangent line to the circle x^2+y^2=9 at the point (1,2 square root of 2). Answered by Penny Nom. 





Two overlapping circles 
20100412 

From Scott: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^2 (half the area of the small circle). The Question is: suppose we have known the radius r of the small circle, and the distance between the two circle centers, what should the radius R of the large circle be? Answered by Chris Fisher. 





An isosceles trapezoid is inscribed in a circle 
20100406 

From Abby: An isosceles trapezoid whose bases have lengths 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid Answered by Penny Nom. 





A max min problem 
20100406 

From Terry: The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere. Answered by Harley Weston. 





A regular hexagon and an equilateral triangle in a circle 
20100405 

From Beth: A regular hexagon and an equilateral triangle are both inscribed in the same circle so that the hexagon and the triangle share three vertices. The radius of the circle is 10cm. What is the difference between the area of the hexagon and the area of the triangle? Answered by Chris Fisher. 





A rectangle inscribed in a circle 
20100324 

From sadiq: here is the question,
in my mathematics book there is equation of the area of the rectangle
inscribed in a circle having equation x^2+y^2=a^2
and the area of rectangle is 4xy=4x(a^2b^2)^1/2
i don't know what is b but a is surely the radius
(i want the derivation for the area of rectangle). Answered by Harley Weston. 





Water in a culvert 
20100318 

From Chip: Hello,
I have a problem to which I know there must be an analytical solution  but as it has been 50 years since I studied math I can't remember quite how to do it!! I have a 12" round culvert in my yard that runs water all year. I would like to be able to calculate the flow through the culvert by measuring the depth of water flowing through and measuring the speed of the current. I can measure the depth and the speed, but I forget how to calculate the cross section of the flow. If you could help I would greatly appreciate it.
Thank you Answered by Penny Nom. 





Two overlapping circles 
20100307 

From Hayden: I have two circles of equal size. The radiuses of the circles are 30ft. The two circles are positioned 40ft apart and I need to find the area where they overlap. Answered by Harley Weston and Tyler Wood. 





A related rates problem 
20100303 

From Amanda: A circle is inscribed in a square. The circumference of the circle is increasing at a rate of 6 inches per second. As the circle expands, the square expands to maintain the tangency. Determine the rate at which the area of the region between the circle and square is changing at the moment when the cricle has an area of 25(pi) square inches. Answered by Penny Nom. 





The equation of a circle 
20100218 

From AHMED: find the equation to the circle with centre at the point (1,1) and touching the straight line 5x+12y=7. Answered by Penny Nom. 





The perimeter of a semicircle 
20100204 

From Sarah: The perimeter of a semicircle is doubled when the radius is increased by 7. Find the radius of the semicircle. Answered by Tyler Wood. 





Bending a wire to form shapes 
20100204 

From Geraldine: a wire bent into the shape of a square encloses an area of 25cm squared. then the same wire is cut and bent into two identical circles. what is the radius of one of the circles round to the nearest hundred Answered by Penny Nom. 





A sector of a circle 
20100204 

From trisha: Given a circle with a radius of 6 inches. Find the area of the sector that is formed by an arc of 36 degrees. Round your answer to the nearest tenth of an inch. Answered by Penny Nom. 





A circular photo in an octagonal frame 
20100113 

From Mike: I have a circle photo 18 and one quarter inches round. I want to cut frame for it in a octagon shape. What would the angle and the length of cut be?
Mike Answered by Robert Dawson. 





The area of a sector 
20100107 

From angelkem: how do you get the area of the circle, the sector, the shaded sector, non shaded sector and its total area if the diameter is 20 cm and each area of the circle is 45 degrees? Answered by Penny Nom. 





A question from a boat builder 
20100101 

From Grant: I am a boat builder, trying to lay out shape of side's elevation.
My question is, how do I define the length of a circle's radius, if I know the chord length
(20 ft) and the segment of the radius between the chord and the circle is known (7 inches)? Answered by Penny Nom. 





Chord length given the length & radius of an arc 
20091231 

From Wayne: Given the length & radius of an arc, is there a formula that will accurately calculate the chord length?
I'm an architectural designer, and would need it explained in layman's terms. Thank you.
Wayne Answered by Penny Nom. 





A circle problem 
20091214 

From Fawad: AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm.
Find the length, in cm of AQ. Answered by Chris Fisher. 





A regular pentagon 
20091214 

From Jamie: A regular pentagon is inscribed in a circle of radius 4.5 cm.
Determine its perimeter and area to one decimal place!
Thank YOU ! :) Answered by Penny Nom. 





An equilateral triangle is inscribed in a circle 
20091206 

From anna: An equilateral triangle is inscribed in a circle of radius 6. Find x and the length of
one side of the equilateral triangle. The picture is a triangle where the corners touch the
sides of a circle and there is a line drawn down the middle of the triangle. A point labeled
D which is in the triangle but im pretty sure that its marking the radius of the circle.
From that point D is a line going from that point to the bottom left corner of the triangle.
So this line shall make another mini triangle. The bottom of the big triangle is then split
into 2 segments and the left segment is labeled x. Please help for I am stuck! Answered by Penny Nom. 





Two overlapping circles 
20091119 

From Raraa: There are two identical circles . The edge of one circle is at the middle point of the other circle. There were overlapped . The area of the overlapped surface is 20000 square centimetres . How do I find the radius of the circle rounded to the nearest whole centimetre ? Answered by Penny Nom. 





A minute hand 
20091105 

From Pardha: A minute hand of table clock is 3cms long. How far its tip move in 20 minutes Answered by Penny Nom. 





A path around a pond 
20091031 

From adeniji: find the area of a concrete path 2m wide surrounding a circular pond 12m in diameter Answered by Penny Nom. 





A line and a circle 
20091019 

From Renson: Determine whether the line x2y=0 cuts,touches or fail to meet the circle x^2+y^28x+6y15=0.If it touches or cuts ,find the coordinates of the point(s) of contact Answered by Harley Weston. 





The equation of a circle 
20091017 

From Renson: A circle passes through (4,2) and (11,5) with center on the line 3y5x+41=0.Determine its equation in standard form. Answered by Penny Nom. 





Concentric circles 
20091014 

From maddy: Find the exact area of the region bounded by two concentric circles with radii 10 inches and 6 inches. Answered by Penny Nom. 





Three circles 
20091002 

From Brandon: There is a quarter circle with a radius of 1. along one eged of it,
there is a semicircl with a diameter of 1, and its center is on the
drawn line. there is another semicircle again with the center on the
other drawn line, and this one has an unknown diameter of X. both
circles are internally tangent, and are tangent to each other. Find X. Answered by Robert Dawson and Chris Fisher. 





Seven circles 
20090920 

From Bobbi: try to put number 1 to 7 in seven circles (one in the middle, 3 on top, 3 below) so the numbers in each row of three circlesvertical, horizontal, and diagonal  add up to 12. Each number can be used only once. Answered by Stephen La Rocque. 





The equation of a circle 
20090830 

From tagbo: find the eqn of circle passing through (1 1) and (1 4)and whose radiusis 5/2 Answered by Stephen La Rocque. 





Two circles 
20090803 

From Karan: We are given 2 circles with radii 12cm and 3 cm. We have to find AB Answered by Penny Nom. 





Circular Measures 
20090724 

From onyeka: find the equation of a circle with point [3,7][5,5] and wich center lies on the line x4y=1 Answered by Robert J. Dawson. 





A degreaser for a fish tank 
20090723 

From charlie: I have a tank that is 10 feet in diameter that I want to put floating degreaser in.The rate for the degreaser is 1/2 gallon per square foot of surface water.How do I figure out how many gallons I need? Answered by Penny Nom. 





A tangent to a circle 
20090714 

From Eric: Hi I am trying to complete a packet that has a list of questions to brush up on precalculus skills. The question asks "For the circle x^2 +y^2 + 6x  4y + 3 = 0 find : the equation of the tangent at (2,5). I have already found the equation for the circle and standard form and the center and radius. However, i do not know how to find the slope or yintercept of the tangent line. Please help. Thanks. Answered by Stephen La Rocque. 





Two chords 
20090711 

From Sarah: Two parallel chords in the same circle have lengths of 30 cm and 48 cm. The circle has a radius of 25 cm. How far apart are the chords? Answered by Penny Nom. 





Arc length 
20090710 

From farhad: hi
i need to measure length of arc by having only two measurements, first the length of the chord and
the height of the curve.
if i have a simple calculator that haven't sin cos tang (i want to calculate it in my mind) Answered by Stephen La Rocque. 





A circle and a chord 
20090710 

From Paul: I have three known points. X1,Y1 = 0,0 X2,Y2 = 3,1 and X3,Y3 = 10,0. Given these three points, how do I find the height from the center of the 10' chord to the circle's circumference above? Answered by Stephen La Rocque and Harley Weston. 





Two circles on a dome 
20090701 

From Beth: My question is related to a dome I would like to construct, for which I know the circumference of the base: 120ft.
I now need to figure out the diameters of two smaller circles, one at 20ft along the arc of the dome form the ground,
and the other at 30ft along the arc.
Assuming a true hemisphere, or 180 degrees total arc, how can I calculate these two circumferences?
Beth Answered by Stephen La Rocque. 





A maxmin problem 
20090420 

From Charlene: A fixed circle lies in the plane. A triangle is drawn
inside the circle with all three vertices on the circle and two of the vertices at the
ends of a diameter. Where should the third vertex lie to maximize the perimeter
of the triangle? Answered by Penny Nom. 





A circle tangent to the Xaxis 
20090329 

From Kiera: Find an equation of the circle that satisfies the stated conditions.
Center C(4,1), tangent to the xaxis Answered by Penny Nom. 





A rolling wheel 
20090329 

From Jules: How far does a wheel of radius 2 feet roll along level ground in making
300 revolutions? Answered by Penny Nom. 





The diameter of a roll of plastic 
20090324 

From truong: hi. i have trouble to calculate the diameter of the plastic roll. the sheet is 765 m long and 0.8 mm to wrap around the core 400 mm in dia. please help me with the formula to calculate the dia of plastic roll, thanks in advance Answered by Harley Weston. 





The radius of a circle 
20090322 

From Justin: Find the radius of a circle with a circumference of 9.43cm. Answered by Penny Nom. 





A regular decagon is inscribed in a circle 
20090312 

From Renata: A regular decagon is inscribed in a circle of diameter 36 feet. Approximate the perimeter and area of the decagon. Answered by Robert Dawson. 





A goat in a square paddock 
20090210 

From lachlan: A farmer uses a rope to tether a goat to a pole at the corner of a square paddock. The length of one side of the square is 24m.
a) If the length of the rope is 12m,what % of the paddock can the goat reach? is the answer 19.62 %?
b) If the farmer wants the goat to be able to graze exactly half the area of the paddock, what length must the rope be? Answered by Penny Nom. 





A regular hexagon is inscribed in a circle. 
20090126 

From Thejas: A regular hexagon is inscribed in a circle. If the perimeter of the hexagon is 42 inches, how many inches are in the circumference of the circle?
How do you express this in the terms of pi? Answered by Robert Dawson and Penny Nom. 





Two tangent circles 
20090123 

From Murtaza: Two circles touch externally at T. A chord of the first circle XY is produced and touches the other at Z. The chord ZT of the second circle, when produced, cuts the first circle at W. Prove that angle XTW = angle YTZ. Answered by Robert Dawson and Chris Fisher. 





A cyclic quadrilateral 
20090123 

From Murtaza: Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively.Prove that the quadrilateral ADEB is cyclic. Answered by Robert Dawson and Chris Fisher. 





Two chords in a circle 
20090119 

From azlaan: prove that line joining the midpoint of 2 equal chords substain equal angle with the chord? Answered by Robert Dawson. 





A wooden deck around a pool 
20090109 

From lupio: a 20' pool is surrounded by a 3' wood deck, find the amount of material needed for the project Answered by Robert Dawson and Penny Nom. 





A chord 
20090101 

From Deepa: Why in a circle,a chord is called as the longest diameter?
(A chord does not passes through the centre of the circle but a diameter passes through the centre) Answered by Penny Nom. 





Three circles inscribed in a circle 
20081218 

From seema: three equal circles each of radius 1 cm are circumscribed by a larger circle.find the perimeter
of circumscribing circle? Answered by Robert Dawson. 





The centroid and circumcircle of a triangle 
20081209 

From prateet: in an equilateral triangle prove that the centroid and centre of the circumcircle coincide
here i am not clear about the concept of centroid and circumcircle
i cant understand how AGis 2/3 AD.
please help in details about the topic mentioned. Answered by Harley Weston. 





Two tangent circles and common tangents 
20081201 

From Alan: Radius of big circle 30cm, radius of small circle 10 cm. From the diagram, the radius from the tangent do not form a semicircle but at an angle. Find the perimeter of the band around both the circle. May need to use trigonometry to find reflex angle AOB, CMD and get the major arc length AB and minor arc length CD Answered by Penny. 





Two tangents to a circle 
20081126 

From rogerson: The length of the tangent to a circle is 15 cm. If the angle between the two tangent lines to the circle is 28 degrees, what is the radius of the circle? Answered by Penny Nom. 





Four circles in a square 
20081119 

From Anthony: I have a square where one side measures 10cm and within that square
There are four equal quarter circles. Each quarter circles starts in a
different corner of the square and I am trying to find area inside the
overlap on the quarter circles. Answered by Janice Cotcher, Chris Fisher and Penny Nom. 





A circle and a chord 
20081117 

From Lydz: The circle has a radius of 8cm
The chord is 13cm long.
Find the distance from the centre of the circle, to the chord. Answered by Penny Nom. 





A circle and a chord 
20081113 

From jane: the center of a circle is at (3,2) and its radius is 7. find the length of the chord, which is bisected at (3,1). Answered by Penny Nom. 





A circle tangent to a line and with its centre on another line 
20081101 

From liza: Find the equation of the circle of radius squareroot 26 tangent to the line 5x+y=13 and having its center on the line 3x+y+7=0. Answered by Chris Fisher. 





The diameter of a circle 
20081101 

From lupito: a circle has a 30`sector,33pi.find the diameter of the circle.How do I set the equation up. Answered by Victoria West. 





How far does the ball travel? 
20081101 

From Betty: This is a question that is perplexing me. I tried to solve it with the Pythagorean Theorem but have not been able to get the right answer. A ball attached to the moving end of the 5meter arm of a pendulum. The pendulum swings through a 90 degree arc once. Approximately how far, in meters, does the ball travel? Answered by Victoria West. 





A canal with cross section a semicircle 
20081019 

From Connor: a canal with cross section a semicircle is 10m deep at the centre.
Find an equation for the semicircle and use it to find the depth 4m
from the edge Answered by Penny Nom. 





Area of a semicircle 
20081006 

From Benjamin: How do you find the area of a semicircle if the diameter is a variable. Answered by Penny Nom. 





How many parallel tangents may a circle have? 
20080929 

From Manish: how many parallel tangents may a circle have? the text book shows two.but a circle can have infinite tangents.then why not parallel tangents coz
theoretically each tangent have a parallel tangnts then no. of parallel tangent a circle may have is equals to half of the infinity i.e. infinity.. Answered by Walter Whiteley. 





The area of an arched transom 
20080928 

From Ivan: What is the formula for figuring out the square footage of arched transom windows & doors? Answered by Harley Weston. 





5 units from (1,2) and 5 units from yaxis 
20080926 

From Shaun: Find the points (x,y) in the plane that are 5 units from (1,2) and 5 units from yaxis.
I am more interested in the approach, in general terms, than the numerical values. Answered by Penny Nom. 





The region between two circles 
20080924 

From Carol: Good day!
Here is a picture of the problem that we need to solve. (I send the picture through email.)
A small circle is inside a larger circle, the only given in the problem is the chord of the larger circle tangent to the smaller circle which measures 16cm. The question is, what is the area of the shaded region?
Can you answer this question? Thanks! :) Answered by Harley Weston. 





Parallel Tangents 
20080924 

From manish: how many parallel tangents may a circle have? the text book shows two.but a crcle can have infinite tangents. Answered by Janice Cotcher. 





The area of a garden 
20080920 

From Hannah: How do you find the area of a semi circle when no measurement is given?
The question is find the area of the garden which is semi circular.
The measurements are 24m and 26m and the semi circle's height is 10m! Answered by Penny Nom. 





An exclusion zone around a triangle 
20080907 

From Awrongo: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Stephen La Rocque and Penny Nom. 





A tangent to a circle 
20080906 

From Jake: Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2) Answered by Penny Nom. 





Half a circle 
20080904 

From brandon: what are the area and perimeter and area of half a circle?? Answered by Penny Nom. 





The length of an arc 
20080904 

From Angie: Segment PR is a diameter of circle S. If angle P =3D 25, find minor
arc QR.
This circle has an isosceles triangle in it, it is connected to the
diameter, Answered by Harley Weston. 





Largest Inscribed Rectangle 
20080903 

From astrogirl: find the shape and area of the largest rectangle that can be inscribed in a circle of a diameter a=2 Answered by Janice Cotcher. 





A triangle and an inscribed circle 
20080901 

From Nancy: I'm a computer programming student, and I'm supposed to figure out how to find the area of a circle inside a triangle if someone types in the length of each side of the triangle.
So, a user can type in any three numbers they want into the three "side length" boxes, and I have to find the area of the circle that would fit inside the triangle they create from those values.
So the circle can be any size, depending on the size and shape of the triangle the user creates. The circle has to touch all three sides of the triangle somewhere. Then, my program calculates the area of the triangle and thus the area of the circle. I just need to know how the circle would change depending on the length of each side of the triangle that the user puts in. Is there a way to find out how the circle's area is related to the triangle around it? Answered by Chris Fisher. 





Radii and Chords Create a NonRight Triangle 
20080822 

From Beary: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. Answered by Janice Cotcher. 





Two tangent circles 
20080822 

From Michele: A circle of radius 2 is externally tangent to a circle of radius 8,
How do you find the length of their common tangent. Answered by Penny Nom. 





Irregular polygon and Circle that Intersects All Sides 
20080820 

From Xetro: Hi,
Suppose you have an irregular polygon(convex or concave) with n > 3 sides.
The question is  Find some circle that will cut(in limiting case  touch) all the sides of that polygon.
It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it.
How to find such a circle? or how to decide if such circle even exists?
What if those segments do not form a polygon but are some arbitrary segments ?
Really want to know how to do it................
Thanks a lot..
Regards,
Xetro Answered by Janice Cotcher. 





Subdividing a chord 
20080818 

From austin: Here is my question. Imagine I have a circle of known radius 25 feet, and a
chord with a mid point height of 6 inches from a central point on the chord
to the circumference of the circle. I wish to divide this chord into a
number of equal divisions. How can I calculate the measurement of the
perpendicular line at each division of the chord to the circumference and at
a 90 degrees at each division Answered by Penny Nom. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





Area of triangle formed by three tangent circles 
20080731 

From brian: Three circles with radii 3,4 and 5 touch each other. The circles are tangent to each other. What is the area of the triangle formed by the centers of the circles? Answered by Stephen La Rocque. 





Inscribed Rectangle 
20080730 

From Felicia: A rectangle whose base is twice its altitude is inscribed in a circle whose radius is 5 mm.
Find the area of the rectangle. Answered by Penny Nom. 





An isosceles triangle inscribed in a circle 
20080715 

From Anne: Here is the math problem quoted from book:
"An isosceles triangle is inscribed in a circle of radius R,
where R is a constant. Express the area within the circle but outside
the triangle as a function of h, where h denotes the height of the triangle." Answered by Penny Nom. 





The length of an arc 
20080714 

From Chris: trying to find the length of an arc or segment of a circle when
the radius or circumference is unknown
take a circle, put a line across the circle label it A /B /C
A and C are the end points, B is the middle
line length is 86. From B to the side of circle is 16. Label that point D
need to find the length of A D C Answered by Penny Nom. 





A tangent line to a circle 
20080709 

From Rita: The tangent to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b, show
r^2(1 + m^2) = b^2 Answered by Harley Weston. 





CIRCLES 
20080707 

From daryl: Find the equation of the smaller circle that is tangent to the axes and the circle x(squared)+y(squared)=2x+2y1? Answered by Penny. 





Two triangles and a circle 
20080703 

From Anita: An equilateral triangle with side of length 1 cm is inscribed in a circle. A second equilateral triangle is circumscribed about the circle with all sides tangent to the circle. Find the length of a side of the second triangle. Answered by Harley Weston. 





A fivesided coin 
20080629 

From carla: A new fivesided coin is to be made in the shape of figure 8.6
The point A on the circumference of the coin is the centre of arc CD, which has a radius of 2cm
Similarly B is the centre of arc DE, and so on.
Find the area of one face of the coin. Answered by Harley Weston. 





A circle inscribed in a square acre 
20080619 

From Scott: Q'm trying to find out the sq footage of the corners of an acre. If an acre is 43,560 sq and if I have this right the surface area of the circumference is 1040 ft. what is the combined square footage of the 4 corners? Or the percentage the original acre? Answered by Harley Weston. 





A space camera circles the Earth 
20080616 

From Rita: A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.
(a) Find an equation that relates the central angle theta to the height h.
(b) Find an equation that relates the observable distance d and theta.
(c) Find an equation that relates d and h.
(d) If d is to be 3500 miles, how high must the camera orbit above Earth?
(e) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen? Answered by Penny Nom. 





If the arc is 75mm, what is the radius? 
20080612 

From malcolm: If the are is 75mm, what is the radius? Answered by Janice Cotcher and Harley Weston. 





Two circles 
20080610 

From cey: the diameter of the larger circle is 20cm, and the smaller 10cm. what is the shaded area?? Answered by Janice Cotcher. 





An ellipse and circle with the same area 
20080609 

From Michael: The area of the ellipse if equal to the area of a circle with radius=40 ft.
Find the values of a and b using appropriate algebraic techniques, not basic math computations.
A=pi ab and satisfy the constraint a+b=100???? Answered by Penny Nom. 





Three mutually tangent circles 
20080604 

From Jacob: If three circles are mutually tangent, does that mean that the two tangent lines are perpendicular? Answered by Chris Fisher. 





How many bricks I can place around a 26inch circle? 
20080522 

From Jon: I want to know how many bricks I can place around a 26inch circle? There must be a formula other than trial and error. The length of the bricks is 6inches. [How many 6inch tangents can be in a 26inch circle?
Thank you very much.
Jon Answered by Harley Weston. 





A triangle inscribed in a semicircle 
20080519 

From Larissa: Find the area of the shaded region outside of a triangle inscribed (meaning the all three points of the triangle are on the circle ) in a half circle of diameter 10 inches, if one side of the triangle is the diameter and the other side is 8 inches long. (A triangle that is inscribed in a triangle is a right triangle by definition.) Answered by Penny Nom. 





The wedges in a circle graph 
20080518 

From Libby: I don't understand how to do this word problem:
The cafeteria workers distributed a survey to the student body asking students to pick 1 from a list of 5 choices for their favorite lunch. The circle graph below gives the results of the survey for the students who responded. What is the measure, in degrees, of the central angle for each choice?
And there is a pie chart that has food choices with these percentages: 25%, 20%, 15%, 10%, and 30% Answered by Leeanne Boehm and Penny Nom. 





The length of an arc 
20080512 

From patricia: Find the length of the arc on a circle of radius r = 16 inches intercepted by a central angle [theta] = 60 degrees Answered by Penny Nom. 





The area of a sector of a circle 
20080510 

From lupio: a problem asks for the area of a sector in a circle,no central angle,in circle is given only 5cm radius, three answers 1809035
can't find a way to start.Help Answered by Harley Weston. 





The distance from the chord to the centre 
20080504 

From sle: What is the method for figuring this type of question out?
in a circle whose radius is 25, a chord has a length of 40. find the distance of this chord from the center of the circle Answered by Penny Nom. 





The diameter of a circle 
20080428 

From Mary: What is the diameter of a circle if the area is 132.7 square meters? I have tried the formula C=2 times pi radius and came up up 21.1. I also tried C = pi times d and came up with 42.26. The answer in the book says 13. How did they get this answer? Thank you for your help. Answered by Penny Nom. 





A rectangle inscribed in a circle 
20080427 

From sridhar: A rectangle with perimeter 28 cm inscribed in a circle of radius 5 cm
find the area ? Answered by Penny Nom. 





A circle inscribed in a triangle 
20080426 

From Amar: I have been given a circle inscribed in a triangle and have been told to prove that the ratio of the perimeter of the triangle to the circumference of the circle is the same as the ratio of the area of the triangle to the area of the circle. How would this be done? Answered by Stephen La Rocque and Walter Whiteley. 





Two overlapping circles 
20080426 

From Michelle: Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ. Answered by Penny Nom and Walter Whiteley. 





The radius of a circle 
20080425 

From kathy: How do you find the radius of a circle if the area is 803.84 and using 3.14 for pi. Answered by Penny Nom. 





Two intersecting circles 
20080417 

From Muhammad: Hi, how can we find the perimeter and area of the region common to two intersecting circles of radii 6 cm and 4 cm with centers 7 cm apart. Answered by Harley Weston. 





A tangent to two circles 
20080413 

From erson: find the length of the tangent segment AB to two circles whose radii are a and b respectively, when the circles touch each other.
the illustration looks like this...hope you'll understand...
there are 2 circles  one is big one is small. they touch each other. and there is this irregular 4 sided polygon that connects them...there is a line that connects them from their center point and another from the tip of the circles...and that's it...i cannot explain very well
please bear with me Answered by Stephen La Rocque. 





A tangent to a circle 
20080413 

From rogerson: Line t from point P is tangent to circle O at T, the point of tangency. Find the length of PT when the radius of the circle is 5cm and the distance between points P and O is 8cm. Answered by Stephen La Rocque. 





Finding the radius when only given chord length 
20080403 

From Lorraine: There are two chords in a circle, an 8 inch chord and a 10 inch chord. The 8 inch chord
is twice the distance from the center as the 10 inch chord. What is the radius? Answered by Stephen La Rocque. 





The area of a circle 
20080403 

From Norm: how to compute the square footage of a circle Answered by Penny Nom. 





Circles and semicircles 
20080323 

From sally: Hi i am sally ,
i need to know what is the formula of :
Find perimeter and area of a semicircle ?
Find the area of a circle whose circumference ? Answered by Penny Nom. 





Angles subtended by the same arc 
20080323 

From Reid: Prove that two inscribed angles subtended by the same arc are equal. Answered by Stephen La Rocque. 





The radius of a circle 
20080322 

From danny: waht is the radius of a circle, if the circumference is 800? Answered by Penny Nom. 





A pentagon inscribed in a circle 
20080319 

From Elaine: My question as written on my homework is: Given a pentagon inscribed in a circle of radius r, determine a) the angle between any two sides of the pentagaon b) the perimeter of the pentagaon c) the area of the pentagon. I know this kind of counts as three questions, so if you can only answer one, that's okay. Any help will be much appreciated. Thanks! Answered by Stephen La Rocque. 





Any regular polygon inscribed in a circle 
20080317 

From lindsay: how do find the perimeter of a regular octagon inscribed in a circle with a radius of 5 units Answered by Stephen La Rocque. 





A circle and a square 
20080312 

From mae: what are the formulas on getting the area of the square outside an inscribed circular region? Answered by Penny Nom. 





The centre and radius of a circle 
20080312 

From Ryan: hello and thank you for such a wonderful service.
This problem I think needs to be checked could you take a gander at it and tell me if i get it correct thanks
find the center and the radius of this circle x^2+y^2=8x2y+15=0
I cam up with center 2, 1/2 and a radius of 11 3/4 Answered by Harley Weston. 





A common chord to two circles 
20080309 

From shubha: please help me out with this problem.
find the length of the common chord of the intersecting circles x2+y24x5=0
and x2+y22x+8y+9=0 Answered by Stephen La Rocque. 





Two circles and a triangle 
20080307 

From Adrian: The vertices of a rightangled triangle are on a circle of radius R and the
sides of the triangle are tangent to another circle of radius r. If the lengths
of the sides about the right angle are 16 and 30, determine the value of
R+r Answered by Penny Nom. 





The diameter of a circle 
20080303 

From Kathie: I know the length of the curved portion of a semicircle is 200 ft. but I need to find the diameter to get a total perimeter and area. How do I find the diameter to get the perimeter? Answered by Penny Nom. 





The perimeter of a sector of a circle 
20080228 

From erica: What is the perimeter of a sector if the radius is 18 and the middle arc is 150? Answered by Penny Nom. 





The radius of a circle 
20080228 

From SteVonee: Estimate the radius of a circle with the given circumference that is 192ft Answered by Penny Nom. 





The circumference and radius of a circle 
20080210 

From Ray: How do you find the circumference or radius of an area presuming it is a circle. Or in other words how do you find the c or r given only the area is 50 sq metres Answered by Penny Nom. 





A chord of a circle 
20080207 

From Mahesh: find the length of the cord intercepted by a circle with equation X2 +Y2 6X+4Y12=0 with a line of equation 4X3Y+2=0
Pl help me solve this problem
thanks
MNK Answered by Stephen La Rocque. 





The equation of a circle 
20080205 

From aime: Find the equation of the circle tangent to 3x+4y15=0 at P1(1,3) and passing through P2(6,3) and P3(0,5)? Answered by Stephen La Rocque. 





The perimeter of a semicircle 
20080202 

From Lisa: How do you find the perimeter of a semi circle when you are only given
the diameter, say 24 units? Answered by Penny Nom. 





Finding the area of an isosceles triangle given one angle and the inradius 
20080124 

From Saurabh: Given an isosceles Triangle, whose one angle is 120 and inradius is √3. So area of triangle is? Answered by Stephen La Rocque. 





Two circles in a rectangle 
20080118 

From Alex: One side of a rectangle is 10 and the other is x.
Two circles with equal radii are inscribed in the rectangle and like a Venn Diagram, the circles overlap.
Each circle touches the top and bottom of the rectangle and the left circle touches the left side of the rectangle and the right circle touches the right side of the triangle.
The distance between the centre of each circle is 2x/3.
Find x Answered by Penny Nom. 





A sector of a circle 
20080117 

From Amandsa: What is the formula for finding the sector of a circle? Answered by Penny Nom. 





A large concrete shape 
20080116 

From Keith: what is the cubic yards of an area that is not a perfect 1/4 circle?
The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth? Answered by Stephen La Rocque. 





The area of a sector of a circle 
20080111 

From Serenity: A denotes the area of a sector of a circle of radius r formed by the central angle theta.
Find the area A if r=10 meters and theta = 1/2 radians. Answered by Penny Nom. 





A circle of diameter 12 cm 
20080111 

From Marcy: The diameter of the circle is 12cm. I need to convert the diameter to m2. Answered by Penny Nom. 





Seven circles in a circle 
20080110 

From fae: what is the area of the remaining portion of a large circle with radius 12cm and the seven smaller and equal circles just fit inside? Answered by Penny Nom. 





A tangent to a circle 
20080104 

From adam: Find a>0 so that the line y=x+a is a tangent to the circle x^2 +y^2=2. Answered by Stephen La Rocque and Harley Weston. 





How would one find the radius? 
20071229 

From Ned: Given an arc with length of 192 inches (don't know chord length),
and arc height of 6 inches, how would one find the radius? Answered by Stephen La Rocque and Harley Weston. 





How many complete revolutions does each wheel make? 
20071228 

From varoon: The wheels of a car are of diameter 80cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66kms per hour? Answered by Penny Nom. 





Circle area 
20071217 

From Marlena: Ok, i do not see how to get the area of circles! they give you the circumfrance
which is 43.96cm and then u have to find the radius and area. I got the area right
which was 7cm but then i got 21.98 for a area and the real answer was 150.39cm
What did i do wrong? Answered by Penny Nom. 





The perimeter of circle 
20071215 

From shaquilla: what is the perimeter of a circle. Answered by Penny Nom. 





A portion of a circle 
20071207 

From Richard: please could you tell me the formula and answer to the following.
I have a circle portion with a radius of 150mm and an angle of 120 deg. If
an arc is drawn from one point to the other as the radii touch the circle
circumference, i need to know the area of the segment and the
formula to carry out the answer.
Many Thanks Answered by Penny Nom. 





A circle inscribed in a triangle 
20071206 

From Linnea: I have a tringle with a circle inscribed in it. My teacher wants me to find the radius of the circle. This is what she gave me to work with. The triangle is ABC, AB = AC = 6, and BC = 4. She also told us to use A(squared) + B(squared) = C(squared). and that there are altitudes and and incenter. I have no idea how to do this. Answered by Harley Weston. 





A radius and a tangent to a circle 
20071204 

From elizabeth: show that the radius of a circle meets a tangent line to the circle in a 90 degree angle.
hint: start by assuming they are not perpendicular and at a contradiction. Answered by Penny Nom. 





The diameter of a gasket 
20071201 

From Jorge: I have an application where I am using a circular silicone gasket. I have the total length but would like to calculate the diameter with the given length. What formula should be used? We receive these gaskets in a roll and cut them about 21 inches and glue the ends together to make it one piece. I would prefer to purchase these already cut and glued but require a diameter. If I had the overall diameter from a 21 inch length gasket, I can look online for a part that comes close to the diameter.
Jorge Answered by Harley Weston. 





Dividing a circle 
20071123 

From matt: hi. can you please send me a diagram of how to draw 3 lines in a circle to get 8 sections. Answered by Stephen La Rocque. 





Find the radius of a circle given the center and a point on the circle 
20071118 

From Raymund: Find the radius if the center is at (0, 5) and one point on the circle is (2,3) Answered by Stephen La Rocque. 





The radius of an arch 
20071110 

From Mark: How do you determine the raduis or diameter of a circle based on the folowing information:
1. The distance along the circle between two points is 35'2". This creates an arch.
2. The (chord) distance between the two points is 30'8".
3. The distance from the center of the chord (on a 90 degree) to the arch is 6'10 3/4". Answered by Harley Weston. 





Constructing the centre of a circle 
20071106 

From Carolyn: I have a line segment AB. I need to divide a segment into 3 parts that are congruent. Please help how to divide it. The answer that I was given previous was not the way the teacher wanted it.
I also need information on how to find the center of a circle given an arc. Answered by Penny Nom. 





Great circles 
20071105 

From Lindsay: Does a sphere have only ONE great circle? Explain? Answered by Stephen La Rocque. 





A circle is inscribed in a square 
20071028 

From Carolyn: A circle is inscribed in a square. What percentage of the are of the square is inside the circle. Answered by Victoria West. 





Hexagon inscribed in a circle 
20071026 

From VIVEK: what are the properties of a regular hexagon inscribed in a circle.
If the radius of the circle is given then how to find the side of the regular hexagon Answered by Stephen La Rocque. 





Arc length and height in a circle 
20071023 

From Bruce: I have been trying to find a formula that relates height of a segment
from the bottommost point of a circle toward the center of the circle to
the corresponding distance along the circumference of the circle
(i.e. at the point on the circumference intersected by a line perpendicular
to that segment). The unknown variable is the height of the segment;
the known variables are the radius of the circle and the distance
along the circumference. Answered by Stephen La Rocque. 





How do you find the radius of a circle if you only know its area 
20071015 

From s: how do you find the radius of a circle if you only know the area of the circle. Do you somehow
reverse the Pi formula. Answered by Penny Nom. 





Finding radius given chord length and distance to center 
20071004 

From Venus: a chord of 48mm long is 7mm from the center of the circle. What is the radius of the circle? Answered by Stephen La Rocque. 





A sheet of corrugated iron 
20071003 

From Ashutosh: A sheet of corrugated iron has corrugations based on the arc of a circle of radius of 3 cm and a central angle of 180 degrees. How many corrugations are formed when a flat sheet of steel 1 metre wide is bent to form a sheet of corrugated iron? Answered by Stephen La Rocque. 





Equation of a circle circumscribing a triangle with given vertices 
20071001 

From Randy: How do I determine the equation of a circle when it is circumscribed by a
triangle whose vertices are (1, 6), (3, 2), and (2, 5)? Answered by Stephen La Rocque. 





Three circles 
20070929 

From Kevin: 3 given circles of R80, R56 & R24 are all in contact. The 2 smaller ones are inscribed in the big one.
Find by calculation or graphically (both if possible) the radiusof a 3rd circle which will be in contact with all 3 given circles. Answered by Chris Fisher. 





A tangent line to a circle 
20070926 

From Randy: Find the equation of the tangent line at coordinates (1 , 4)
on the circle x^2 + y^2  4x  21 = 0
I would like to learn the fastest way to relate any coordinates of a circle
to any possible point of tangency. Answered by Stephen La Rocque. 





A piece of wire is bent in the form of a circle 
20070924 

From Renece: a piece of wire is bent in the form of a circle and it encloses an area of 154cm
a) calculate the radius of the circle
b) the circumference of the circle
use 22/7
The same piece of wire is then bent into a square
d) calculate the area enclosed by the square. Answered by Penny Nom. 





Finding the center of a circle that goes through three given points 
20070916 

From Gary: I am given three points represented by their Latitude and Longitude. How do I determine the Latitude and Longitude of the center of a circle through the three given points?
The lat/lon of the three points are:
A. N 43 degrees 30.251 min. W 96 degrees 45.695 min.
B. N 43 degrees 30.006 min. W 96 degrees 45.082 min.
C. N 43 degrees 30.719 min. W 96 degrees 45.410 min.
Thanks. Answered by Stephen La Rocque. 





The area of half a circle 
20070914 

From Heather: We need the formula for area of half circle please explain where each number comes from. Answered by Penny Nom. 





The circumference of a circle 
20070911 

From annette: circumference of a 3.75 ft circle I have not done this in years and forgot how. Answered by Stephen la Rocque and Victoria West. 





The perimeter of a semicircle 
20070911 

From Confused: What is the formula for the perimeter of a semicircle?
Can you please help me out!!!
I need this answer by tomorrow. Answered by Stephen la Rocque. 





Divide a circle into 5 equal parts 
20070907 

From Kathy: How do you divide a circle into 5 equal parts using a protractor? Answered by Penny Nom. 





The area of a circle knowing only the length of a chord 
20070905 

From James: I need some help in the right directions with a problem. I was presented with a problem where I need to find the area of a circle knowing only the length of a chord.
the is a circle in the center of a larger circle (which the size of either could change) the only thing that matter is that the chord is 100 ft long and rests on top of the smaller circle. Answered by Stephen la Rocque and Brennan Yaremko. 





Another circle problem 
20070827 

From Lindsay: Hello. I'm trying to a math problem and have searched the internet for equations, but have come up empty handed. If you could help, that would be greatly appreciated!
The question is stated thus: Find the equation of the following circle:
the circle that passes through the origin and has intercepts equal to 1 and 2 on the x and yaxes respectively. Answered by Stephen La Rocque and Penny Nom. 





A circle and a tangent 
20070827 

From Lindsay: Hello. I'm trying to do a math problem and have searched the internet for equations but have come up empty handed. If you could help, that would be greatly appreciated!
The problem is stated thus: A circle is tangent to the yaxis at y=3 and has one xintercept at x=1.
a. Determine the other xintercept
b. deduce the equation of the circle. Answered by Penny Nom. 





Reference angles 
20070825 

From Jenny: find the reference angles for the angles given below, find the quadrants in which the angles lie
1. 0=6n/7
2. 0=3.3 Answered by Stephen La Rocque. 





Tangents to a circle 
20070818 

From Laura: I have tangents from point A and B that intersect at C. A third tangent XY lies in between the two lines that I have already drawn. I measured the perimeter and then I drew another line that was tangent to the circle and was inside the two lines again and measured the perimeter again. The perimeters were the same but I don't know how to prove why this happened and write a theorem for it. Answered by Chris Fisher. 





Two circles C1 and C2 meet at the points A and B 
20070815 

From Jerry: Two circles C1 and C2 meet at the points A and B. The tangent to C1 at A meets C2 at P. Point Q inside C1 lies on the circumference of C2. When produced, BQ meets C1 at S and PA produced at T. Prove that AS is parallel to PQ. Answered by Chris Fisher. 





Circle Geometry 
20070814 

From Robin: In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Answered by Stephen La Rocque. 





The equation of a circle 
20070812 

From ranessa: Write the equation of the circle that satisfies the given condition.
C(0,8) ; R = 5 Answered by Penny Nom. 





Chords 
20070808 

From HIMANSHU: we know that every straight line is the chord of a big circle. i have a circle
with radius 3.5feet. I want to know what is the length of the chord,
which would be a straight line. Answered by Stephen La Rocque. 





An athletic track 
20070730 

From tammy: The inner boundary ABCDEF of an athletic track cinsists of two straight parts each 90m long and two semi circular ends as shown in the diagram.If the perimeter of the inner boundary is 400m, calculate the diameter AE of the inner semi circle.
Part 2. If the track is 3.5m wide an athlete starts the 400m run at X and remains in the outer lane . He finishes at Y(1) Calculate the outer diameter YZ
(2)The distance XY (take pie as 22/7) Answered by Penny Nom. 





Two chords in a circle 
20070729 

From Jerry: Points A and C lie on the circumference of a circle. B is a point inside the circle. When produced, AB and CB meet the circumference at points E and D respectively. Prove that AB = CB, then EB = BD. Answered by Stephen La Rocque. 





Circle Geometry III 
20070717 

From Sean: Two rays are drawn from the same point A outside a circle, and intersect the circle as shown in the picture. Prove that the measure of angle A is onehalf the difference between the measures of arcs BD and CE. Answered by Stephen La Rocque. 





The height of an arc at the center 
20070717 

From Bob: I have a circle with a 26" radius and a cord whose length is 20". How can I find the height of the arc at the center point of the cord? Answered by Penny Nom. 





Circle Geometry II 
20070717 

From Sean: Let M be a point outside a circle, and let a line through M be tangent to the circle at point P. Let the line through M and the center of the circle intersect the circle in points Q, R.
Prove that │PM│^{2} = │MQ│ x │MR│ Answered by Stephen La Rocque. 





Circle Geometry  Quadrilateral circumscribing a circle 
20070717 

From Sean: Four lines are tangent to a circle that form a quadrilateral. It appears that the quadrilateral is a trapeziod but this is not a given. Prove that the combined lengths of two opposing sides of the quadrilateral are equal to the combined lengths of the other two opposing sides of the quadrilateral. Answered by Stephen La Rocque. 





Finding the area of a circle from its circumference 
20070716 

From Amanda: what is the area of a circle with a circumference of 3000 metres? Answered by Stephen La Rocque. 





Any regular polygon inscribed in a circle 
20070712 

From DJ: Circle with r=12" is inscribed in a regular octagon. What is the length of each octagon segment?
Note: Our answer works for any regular polygon inscribed in any circle. Answered by Stephen La Rocque. 





Length of a circle 
20070711 

From Debra: i have a radius of 73 inches, i need to know the length of the circle please. Answered by Stephen La Rocque. 





Finding the radius of an inscribed circle 
20070705 

From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher. 





The area of part of a circle 
20070621 

From Sarah: Hi, I need help finding the area of a part of a circle that involves a
chord. I need this answer/help very soon if at all possible. I have
attached a drawing of what I am trying to solve. Thank you for your help!
Sarah! Answered by Penny Nom. 





Area of a circular garden 
20070618 

From Cynthia: Hi is this the correct formula for this problem?
What is the approximate area of a circular garden that is 20 feet in
diameters? Answered by Stephen La Rocque. 





Babylonian geometry 
20070617 

From marleen: The following problem and the solution were found on a Babylonian tablet dating from about 2600BC:
Problem:60 is the Circumference, 2 is the perpendicular, find the chord.
Solution:
Thou double 2 and get 4
Take 4 from 20, thou gettest 16
Square 16, thou gettest 256
Take 256 from 400, thou gettest 144
Whence the square root of 144, 12 is the chord.
Such is the procedure. Modern day mathematicians have reasoned that the Babylonian Mathematician who solved this problem assumed that the value of Pi is 3. By explaining in detail how the Babylonian Mathematician must have solved this problem, justify the reasoning of the modern mathematicians. Answered by Stephen La Rocque. 





What is the size of the circle it would make? 
20070613 

From ed: i have a piece of sheet metal 56' 6" long what is the size of the circle it would make Answered by Penny Nom. 





A sequence of circles 
20070611 

From Ann: Please help with solving the following problem!!!
A circle is inscribed in an equilateral triangle with a side of length 2.
Three circles are drawn externally tangent to this circle and internally
tangent to 2 sides of the triangle. 3 more circles are drawn externally
tantgent to these circles and internally tangent to 2 sides of the triangle. if
this process continued forever, what would be the sum of the areas of all the
circle? the answer 1 parent came up with was Pie over 2, but we don't
know how he did it. Can you please show the work or explain the answer to
this problem?
Thank you
Ann
p s my daughter is in 9th grade math. Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





A circle and polygon with equal perimeters 
20070605 

From matthew: Why does a circle have the largest area of any polygon when the perimeter is always 1000m for every polygon? Answered by Stephen La Rocque and Penny Nom. 





A circle inside a square 
20070531 

From Mer: there is a circle inside a square... there is a shaded rectangle that measures 5mm X 10mm and they want to know what the radius is. The edge of the shaded rectangle touches a point on the circle. Answered by Penny Nom. 





A point on a semicircle 
20070528 

From arun: a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find area of the semi circle? Answered by Penny Nom. 





Discovering the incircle of an irregular polygon 
20070525 

From Joaquim: I've been searching in some books and many websites, but I couldn't find a formula or algorithm for discovering the incircle of an irregular polygon, could you please help me? Answered by Walter Whiteley. 





Relative sizes of circles 
20070522 

From Griselda: There are 4 small circles inscribed in a bigger circle. The larger circle has a radius of 10 cm. Find the radius of the largest circle which will fit in the middle. Answered by Stephen La Rocque. 





Comparing the areas of various shapes 
20070516 

From Kathy: If the perimeters are the same, which has the greater area, a circle, a square, an ellipse, or an octagon? Answered by Stephen La Rocque. 





Area of irregular surfaces 
20070509 

From Dustan: I am working on a way to compute very accurate
areas for irregular surfaces by using the idea of a largest possible circle... Answered by Chris Fisher. 





Area of region between circle and inscribed octagon 
20070507 

From amy: I have to find the area of the shaded region where there is an octagon inscribed in a circle
The radius is 4 inches. The shaded region is everything besides the octagon inside the circle.
How can I find the area of the shaded region?
Thank you! Answered by Stephen La Rocque. 





The circumference of part of a circle 
20070506 

From Wallis: I have more then a quater of a circle, but less than half. What is the circumference if the two side are 7cm and the angle between them is 110 degrees? Answered by Penny Nom. 





A point inside a circle 
20070504 

From edgemitter: There is a point inside a circle (but not in its center) where two perpendicular secants intersect, dividing the circle into four regions with different area. Calculate the area of the four regions Answered by Walter Whiteley. 





Two concentric circles form an annulus 
20070502 

From A student: In the diagram below, two concentric circles form an annulus. The
vertical line is tangent to the inner circle, and forms the diameter of
a third circle.
Explain why the areas of the annulus and third circle are the same. Answered by Penny Nom. 





A square contains five circles with the same radius. 
20070421 

From Jamie: A square has a side length on 1 m.
The square contains five circles with the same radius.
The centre of one circle is at the centre of the square and it touches the other four circles.
Each of the other four circles touches two sides of the square and the center circle.
Find the radius. Answered by Penny Nom. 





Constructing an octagonal deck around a circular pool 
20070420 

From Cliff: [I am building an] octagonal desk encompassing 17 foot diameter circle for pool.
I have seen other octagonal calculations but none of these tell me how much allowance for a circle to fit within the octagon without losing the circle edge can anyone help
thanks cliff Answered by Stephen La Rocque. 





Two concentric circles 
20070419 

From James: Two concentric circles have a chord running through the outer one. The chord is the tangent of the inner circle and is 14 cm.The outer circle is shaded and the inner circle is not. Find the exact area of the shaded region without using a calculator. Answered by Stephen La Rocque. 





Four semicircles are drawn inside a square 
20070419 

From James: Four semicircles are drawn inside a square, with the diameter being the length of the square.The overlapping portion of the semicircles are shaded. What fraction is shaded? Answered by Penny Nom. 





Two tangents to a circle 
20070417 

From Doug: Two distinct, nonparallel lines are tangen to a circle. The measurement of the angle between the two lines is 54 degrees (angle QVP).
Suppose the diameter of the circle is 2 cm. What is the distance VP? Suppose the distance VP is 3.93 cm. What is the diameter of the circle? Find a formula for d, the diameter of the circle, in terms of VP.
Find a formula for VP in terms of d, the diameter of the circle. Answered by Stephen La Rocque. 





Intersection of a line and a circle 
20070412 

From gaby: The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers. Answered by Steve La Rocque and Melanie Tyrer. 





An arc shaped groove into a peice of metal 
20070412 

From daniel: hello i work at an engineering workshop the other night i was asked to machine an arc shaped groove into a piece of metal the cord length was 6 mm and the height from the middle of the cord to the arc was 1mm i was hoping to find the diameter of the cutter needed to do the job and also the formula to work out how to find the diameter. i believe it is 10mm dia thankyou for your time and knowledge Answered by Stephen La Rocque. 





A cabinet with an arched front 
20070409 

From Joe: I am building an arched front cabinet that is 71 inches wide, 12 inches deep at both ends
and 16 inches deep at the center. To accurately build this cabinet I need to known the radius of
the circle that would form that arch.
Thanks,
Joe Answered by Penny Nom. 





Area of circles within a circle 
20070408 

From Avaline: Imagine that there are four small circles inscribed in a bigger circle. The 4 small circles are shaded. What is the ratio of the area of the shaded region to the area of the unshaded region? Answered by Stephen La Rocque. 





An arched opening for a large doorway 
20070408 

From Richard: I am trying to build an arched opening for a large doorway...I know the vertical sides of the opening to be 8'9" from the floor to the lowest point of the arch on each side...I know it is 15 1/2" from the center horizontal point to the top of the arc...I know the vertical sides are 11'11" apart...what I need to know is the radius to create the proper arc. Can you help? Answered by Stephen La Rocque. 





Radius of a circle in a square 
20070405 

From Lori: A circle is inscribed in a square. What is the radius of the circle?
If there is a small rectangle with a 2 ft. top and a 1ft side at the left in the
square touching the corner of the circle. Answered by Stephen La Rocque and Penny Nom. 





A triangular prism 
20070326 

From Tom: Hi, I need to find a container in the shape of a triangular prism that will fit
four table tennis balls (this is for a math project!). These balls have a
diameter of 4cm, so a radius of 2. I know that the formula for finding
an incircle from a triangle is: radius of incircle =
2area of triangle / perimeter of triangle
But I need to know the length of one side of the triangle from the incircle
(the triangle needs to be equalateral).
Can you help me find a formula for this?
Thanks so much!
Tom Answered by Penny Nom. 





Inscribed square in inscribed circle 
20070325 

From Confuzzled: "The largest possible circle is drawn inside a square. Then the largest possible square is drawn inside this circle. What is the area of the inner square as a fraction of the area of the outer square?"
This is a question from the Grade 8 Gauss contest and I don't know how to work it out without drawing it. My teacher says it's possible but I still don't get it. Please help!!! Answered by Stephen La Rocque. 





Circles and chords 
20070315 

From Henry: Where do you place a chord in a circle such that it divides the area
of the circle 1/3 and 2/3? Also, what is the length of the chord? Answered by Stephen La Rocque. 





circles 
20070306 

From chetna: A large circle has a radius of 10cm.Given four congruent circles tangent to one another within the large circle what is the radius of the largest circle which will fit in the middle ? Answered by Stephen La Rocque. 





Cutting the top off a circle 
20070225 

From Daniel: If a circle as a diameter of D I cut off a straight part at C from the top What is the formula to find the area of the left over part? Answered by Penny Nom. 





Circles 
20070222 

From Erika: I have a research paper due on real life uses of conic sections I've looked through all your conic topics and uses of them, but and i cant seem to find real life uses for circles. What are real life uses of circles? Answered by Penny Nom. 





A pentagon inscribed in a circle 
20070222 

From Amanda: Find the formula for calculating the length of the side of a pentagon given the radius of the circle that encloses it. Once you find the formula, find the length of the side of a pentagon which is enclosed in a circle 12 cm in diameter. So I need to know the formula, and the length of the side of the pentagon. Thank you!! Answered by Penny Nom. 





A circle tangent problem 
20070221 

From Jason: Please help me to solve this problem. Thank you very much. Find the equation of the circle tangent to 3x+y+14=0 and x+3y+10=0 with radius squareroot of 10. Answered by Stephen La Rocque and Penny Nom. 





Finding the equation of the circle 
20070220 

From ning: Given the radius of a circle square root of 10 tangent to the line 3x+y+19 = 0 and passing through (0,3), how can i solve the equation of circle? thank you... Answered by Chris Fisher, Steve La Rocque and Penny Nom. 





Two concentric circles 
20070211 

From maria: i have a problem with this quadratic word problem which i am trying to solve it but couldn,t get it please help me to solve this question Two concentric circles are drawn, the radius of one being 2cm greater than that of the other. The area of the ring enclosed between the two circles is one quarter of the area of the smaller circle.Calculate the radii of the circles,correct to three significant figures. (Don,t substitute for pie) Answered by Stephen La Rocque. 





Perimeter of an octagon inside a circle 
20070208 

From Courtney: a regular octagon is inscribed in a circle with a radius of 12 cm. find the perimeter of the octagon? Answered by Stephen La Rocque. 





A triangle inscribed in a semicircle 
20070206 

From Benneth: Consider a triangle inscribed in a semicircle with a radius of R. What are th possible perimeters for the triagle? And the areas? Answered by Penny Nom. 





A rectangle inscribed in a circle 
20070204 

From Benneth: Consider a rectangle with radius R inscribed in a circle. What are the possible areas of the rectangle? Answered by Steve La Rocque and Walter Whiteley. 





The centre and radius of a circle 
20070127 

From A student: x^2+y^2=121 is the equation of the Circle C
(1) Write down the center and the radius of C. Answered by Stephen La Rocque. 





A circle inscribed in an octagon 
20070125 

From Anna: If I know that the sides of my octagon are 8 units, how do I determine the radius of an inscribed circle? Answered by Penny Nom. 





Splitting A Circle Evenly 
20061220 

From Joe: I'm trying to make a game board and instead of having it square, I would like to give it a curve (the game is Parcheesi). The attached diagram is pretty much completed (done in AutoCAD). What I would like to know is how to manually find the points that intersect the red line. In other words, evenly split the semicircle into 8 pieces. Answered by Penny Nom. 





A regular polygon inscribed in a circle 
20061219 

From Katy: If a regular hexagon is inscribed in a circle of radius 6.72 centimeters, find the length of one side of the pentagon. How would I got about explaining this? Answered by Penny Nom. 





Circles and polygons 
20061211 

From Irene: Can you define a circle as a polygon with an infinite number of sides which are infinitely small? If you can, can you then define a cylinder as a prism? The sides would be rectangles or parallelograms with one length infinitely small? Answered by Chris Fisher. 





Area of a circle 
20061201 

From Lisa: i have 24m of fence how would i find out the area of a circle using this 24m of fence? Answered by Stephen La Rocque. 





Sectors of a circle 
20061130 

From Maithreyi : A circle of diameter 21m is divided into three sectors with central angles 60degree,120degree and 180degree. Find the area of each sector? Answered by Stephen La Rocque. 





Creating a triangle in a circle 
20061128 

From Dirk: My daughter has a school project where she must draw a circle and then draw an equilateral triangle inside the circle. She said you have to identify six points on the circle to correctly draw the triangle. How do you accomplish this? Answered by Penny Nom. 





The area of a semicircle 
20061125 

From Melinda: If the radius of a semicircle is 9ft what is the area? Answered by Karen McIver and Penny Nom. 





Circle geometry 
20061119 

From Namrata: AB is a diameter and AC IS A CHORD OF A CIRCLE SUCH THAT angle=30. the tangent at C intersect AB produced in a pointD. Prove that BC=BD. Answered by Stephen La Rocque. 





Conic sections 
20061119 

From Joyce: My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation. Answered by Penny Nom. 





The area of regular pentagon inscribed in a circle 
20061012 

From Admire: i need help on how to find area of regular pentagon inscribed in a circle of radius 8cm Answered by Stephen La Rocque and Penny Nom. 





Is a circle a regular shape? 
20061010 

From David: Is a circle a regular shape or an irregular shape? Answered by Stephen La Rocque. 





Two word problems 
20061002 

From Eve:
1. A surveyor's map shows a plan for the rectangular rose garden whose area is
a^{2}+25ab350b^{2}. Find an algebraic expression for the length and width. If a=20 ft and b=10 feet, find the actual dimensions of the garden.
2.A square is enclosed in a circle. The area of the square is (4r^{2}32r+64)sq cm and the area of the circle is 484r^{2} sq cm. Write a polynomial in factored form to represent the difference of the two areas.
Answered by Stephen La Rocque. 





The area of a circle 
20061002 

From A student: Calculate the area of a circle whose radius is 75 meters? Answered by Stephen La Rocque. 





An equilateral triangle has been wedged in between two circles. 
20060922 

From Kim:
An equilateral triangle has been wedged in between two circles. How does the diameter of the smaller circle compare to the diameter of the larger circle.
image: circle inside of an equilateral triangle touching all sides of the triangle; both the triangle and the circle inside are placed into a larger circle where the triangle vertices all touch the circle
Answered by Penny Nom. 





A concrete semicircle 
20060815 

From John: I have to figure out how many yards of concrete I need for a semicircle. I have a radius of 21 feet and the concrete is 4" thick. I took 3.14 x (21)^2 then divided by 40 to get how many yards of concrete but that doesn't seem right. Answered by Penny Nom. 





What is the area of the circle? 
20060719 

From Nana: the circle is tangent to sides BC and AD of the 8 by 12 rectangle, ABCD. What is the area of the circle? Answered by Stephen La Rocque. 





A tangent to a circle 
20060705 

From Izumi:
I have problems finding the point of tangency between the circle C
x^{2} + y^{2} + 4x  6y  12 = 0
and the tangential line that passes through the point P (6, 1).
Answered by Stephen La Rocque. 





A 9 foot diameter circle 
20060702 

From Lisa: How do I calculate 9 foot diameter measurement in total feet?? Answered by Stephen La Rocque. 





Marking out a circle 
20060628 

From Peter: given a straight line. how do i work out the off sets ( at right angles) at several intermediate points. to set out a 5.0m arc that has a 18.0m radius. Answered by Stephen La Rocque and Penny Nom. 





The area of part of a circle 
20060529 

From Larry: need to find area of a circle between a given line (cord) to the circumference of the circle (see attachment). I often review blue prints of homes and many times have to know the area the home. Answered by Stephen La Rocque and Penny Nom. 





The length of the diameter 
20060518 

From Steven: A circle has a circumference of 312in. Find the length of its diameter to the nearest integer? Answered by Penny Nom. 





The last slice of pizza 
20060427 

From Lori: I have a pizza. The radius is 10 inches long.The pizza was cut into 16 equal slices. When one slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.
How far up the radius from the center of the circle will I need to cut so we will both have an equal area of pizza? Answered by Stephen La Rocque. 





Geometry proof 
20060423 

From Jade: From a point P outside a circle with centre O, tangents are drawn to meet the circle at A and B.
a) Prove that PO is the right bisector of the chord AB.
b) Prove that Answered by Stephen La Rocque. 





Which has more pizza? 
20060419 

From Kristine: Which has more area: a round pizza that is 16 inches in diameter or three square pieces of pizza that are 8.5 inches on each side? Answered by Stephen La Rocque. 





Three circles inside a larger circle 
20060416 

From Meghan: Given three congruent circles tangent to one another (radii = 1), what is the radius of a circle circumscribed around them?
Answered by Stephen La Rocque. 





Overlapping area of two circles 
20060415 

From Jade: Given two identical circles where the radius (6 units) is the distance between the centers, what is the area of the overlapping region?
Answered by Stephen La Rocque. 





An epicycloid 
20060410 

From Sharon: What is the name of the curve formed by a point on the circumference of a circle that rolls on the outside of a fixed circle? This curve is used in the study of gears. Answered by Stephen La Rocque and Penny Nom. 





Two circles 
20060407 

From Louisa: One circle of radius 7cm is touching another circle of radius 4cm. These circles are on a line and the problem is to find the length AB where A is the point marking the bottom of the radius of one circle and B is the point marking the bottom of the radius of the other circle. Answered by Stephen La Rocque. 





A square in a circle 
20060405 

From Lisa: A square is inscribed in a circle. Determine the percent of the circle's area that is outside the square. Answered by Stephen La Rocque. 





The centre and radius of a circle 
20060402 

From Kaye: I need to calculate Dimension E and F. I am given A, B, C, (or over all A+B+C), D, G. The radius is one continuous unknown radius.
Example: A = 23.50
B = 35.50
C = 0.50
D = 11.50
G = 23.50
I have calculated this for angles but my mind is drawing a blank for the radius calculation. I can draw it but I need to put into Excel spreadsheet.
Answered by Harley Weston. 





Can one divide a circle into 4.5 parts 
20060330 

From Chris: If it is possible, can one divide a circle into say, 4.5 parts (with 4 equal parts and a half part)?
Or for that matter, for any integer, n, into n/2 parts as above?] Answered by Walter Whiteley. 





The square footage of an area in my backyard 
20060317 

From Kim: I need to find out how to calculate the square footage of an area in my backyard that is in the shape of a "slice of pie". There are two sides that are straight lines that come together at the top to form a point, and then at the bottom is a curved line that joins the two other lines together. I need to figure out how to calculate the square footage that is inside the area. Answered by Penny Nom. 





If a circle is elongated into an oval .. 
20060316 

From Bruce: If a circle is elongated into an oval, with constant circumference, does the area remain constant? Answered by Walter Whiteley. 





A circle containing two points 
20060313 

From Skye: Write the equation of a circle having area 15pi and containing the points (1, 5) and
(1, 9). Answered by Penny Nom. 





What names are known for the quarter circle shape? 
20060306 

From Christina: What names are known for the quarter circle shape? Answered by Stephen La Rocque and Penny Nom. 





Make 2 rows of 4 circles with only 6 circles 
20060131 

From Sarah: Moving as many circles as you need, make 2 rows of 4 circles only having 6 circles? Answered by Chris Fisher. 





Sectors and arcs 
20060125 

From Wael: How is the area of an arc (alpha*pi*r squared/360) derived?
How is the length of an arc (alpha*pi*r/180) derived? Answered by Penny Nom. 





A circle problem 
20060123 

From Matyan:
Find the standard equation of the circle that passes through the points (0,4) and (3,7) with center on the line
2xy+4=0.
I've tried substituting the two points to the general equation of a circle, but I can't solve it without a third equation. The problem here is I don't really know how to use the given line of 2xy+4=0. Please help. Thank you.
Answered by Penny Nom. 





The circumference of a larger circle is twice the circumference of a smaller circle. 
20060120 

From Amanda: The circumference of a larger circle is twice the circumference of a smaller circle. What is the ratio of the radius of the smaller circle to the diameter of the larger circle? Answered by Penny Nom. 





A sequence of circles and tangents 
20060116 

From Paul: Consider a circle whose center is (2,2) and whose radius is 1, and the
straight line that goes through the origin and that is tangent to this
circle so that the intersection between them is as shown in the attached
picture. With this new point we make a new circle whose radius is half
of the first one, and we calculate the corresponding intersection point
with the same suppositions as in the first case. We repeat the process
to the infinite. Find the distance between the center of the circle in
the infinite and the origin (point (0,0)). Answered by Chris Fisher. 





The area of a sector of a circle 
20060102 

From Natashia: How do you find the area of a shaded sector of a circle? Answered by Penny Nom. 





A goat is tied to the corner of a 50 ft square outbuilding 
20051224 

From Danielle: Topic: A goat is tied to the corner of a 50 ft square outbuilding with a 40 ft. rope.
a) What is the measure of the partial circumference created as the goat walks at the full length of the rope?
b) Since the goat is trimming the grass from part of the outbuilding, how much of the perimeter of the outbuilding will the building owner have to trim? Answered by Penny Nom. 





A regular octagon is inscribed in a circle 
20051213 

From Carlin: A regular octagon is inscribed in a circle of radius 15.8 cm. What is the perimeter of the octagon? Answered by Penny Nom. 





Four tangent circles 
20051206 

From Ananth:
I have one bigger circle A with radius 15.
Inside this bigger circle i have another circle B with radius 3 which touch this bigger circle. Have another circle C with radius 4 which touches A and B. I would like to draw a biggest circle which touches A,B and C.
Answered by Chris Fisher. 





Divide a circle into eleven parts 
20051107 

From Dean: I would like to know how to divide a circle into eleven parts using only four lines. Answered by Claude Tardif. 





The length of a chord 
20051103 

From Sue: How do you determine the length of a chord when given the diameter of the circle (1.6m) and that the angle = 7π/8 Answered by Penny Nom. 





A line that intersects a circle 
20051018 

From Bruce: I would like to solve the following problem illustrated below. How do you calculate the length of a line that intersects a circle. Answered by Penny Nom. 





The area of an irregular semicircle 
20051014 

From Bob: Is there a way to compute the area of an irregular semicircle i.e. one in which the arc length is not determined by the diameter; and is therefore not technically any part circular  yet still possessing an arched side? Answered by Penny Nom. 





Calculer la clé 
20050929 

From Un eleve: Chaque individu a un numéro INSEE de 13 chiffres auquels est adjointe une clé de deux chiffres.
voici comment est calculée cette clé : Answered by Claude Tardif. 





The length of a circle's chord 
20050928 

From A homebuilder: find the length of a circle's chord with a known arc length and radius/diameter lengths. Answered by Penny Nom. 





The radius of an arc 
20050819 

From Jared: I need to be able to calculate the radius of an arc on an existing structure (Supports for Fifth Ave Dimensional Text). I have the overall length of this structure, but, the complication I believe lies in the fact that it is a curve mounted onto a flat section of wall on either side of a very mild curve, therefore, measuring the middle of the wall to the top of the arc does me little good...The reason I need this is to be able to replicate the above curve on a similar structure to be mounted below it...Also, because the client wants the structure mounted on the inside of the opening below the existing, the beginning and end point of the new structure would be lower than the existing, so, I do not believe that it is possible to exactly replicate the radius of the above curve? Answered by Penny. 





Is 360 Really the correct value? 
20050815 

From Jack: Considering the circumference of a "Perfect Circle" with a Diameter of 1 meter would be something like 3.14 meters, why do we use the number 360 to represent the number of degrees within that circumference?
Would it not make more sense to express the degrees in reference to the relationship to the diameter as related to pi?
That is, let's just say our "Perfect Circle" has a circumference of 3.14 meters, therefore, what we now consider as due east would change from 90 Degrees to 78.5 Degrees. Answered by Penny Nom. 





Framing an arched wall 
20050812 

From Mike: I'm framing a building wall with a curved (arcing) top section. The radius of the section is 74'6" with a height above finish floor of 16'0". The horizontal run of the arced section is 23' 1 1/2" with a low height above finish floor of 12'4". If I start with a 16' stud at the high end how long are the subsequent studs if they are on 16" centers? Short of laying this out on a tennis court how can I work out the lengths of the studs? Answered by Penny Nom. 





Two tangents to a circle 
20050618 

From Tej: The tangents drawn from points M and N of a circle
having centre O intersect each other at point P. If
angle MPN=60 degrees, NM=10, then find the radius of
the circle and Area of quadrilateral OMPN. Answered by Penny Nom. 





Difference in latitude 
20050405 

From Gretel: Assuming the the earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 400 kilometers due north of the other? 500 kilometers? Answered by Penny Nom. 





Two overlapping circles 
20050320 

From Safi: I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle. Answered by Penny Nom. 





Tangents to a circle 
20050319 

From Sue:
You're given the equation to a circle (x3)^{2 }+ (y3)^{2} = 4
and you need to do 3 things:
1. Find a point on the circle
2. Construct an equation for a tangent line to the circle and through the point
3. Plot the circle, point and the tangent line on one graph
Answered by Penny Nom. 





Three tangent circles 
20050125 

From Kate: Two circles, C1 and C2, touch each other externally; and the line l is a common tangent. The line m is parallel to l and touches the two circls C1 and C3. The three circles are mutually tangent. If the radius of C2 is 9 and if the radius of C3 is 4, what is the radius of C1? Answered by Chris Fisher. 





The diameter of a 800 km circle 
20050122 

From Mechelle: What is the diameter of a 800 km circle? Answered by Penny Nom. 





The radius of a circle 
20050118 

From A student: find the radius of a circle whose area is 1256sq cm.Use pi as an appoximation for pi. Answered by Penny Nom. 





A nonrerctangular lot 
20050118 

From EM: One corner of a 60X120 foot lot, otherwise rectangular, is a curve with a radius of 20 feet and a central angle of 90 degrees. What is the area? Answered by Penny Nom. 





The length of a chord 
20050113 

From A parent: Does anyone have a formula for calculating the chord length for a segment of a circle when you know the radius and the enclosed angle or radian ? Answered by Penny Nom. 





Arcs and chords 
20050109 

From Aniesha: A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. Find the radius? Answered by Penny Nom. 





A line from the center of the patch to the periphery 
20050101 

From Sandrine: I am currently researching a patch disease of grasses. These patches are roughly circular. I need a term for a line from the center of the patch to the periphery. Since the patches are not perfectly circular, my supervisors tell me I cannot use the word 'radius'. What else could I use? Answered by Denis Hanson and Harley Weston. 





Irrigation and a sector of a circle 
20041223 

From Chuck: A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres. Answered by Harley Weston. 





A regular hexagon is inscribed in a circle. 
20041208 

From Abraham: A regular hexagon is inscribed in a circle. What is the ratio of the length of a side of the hexagon to the minor arc that it intercepts?
(1) pi/6
(2) 3/6
(3) 3/pi (This is the correct answer.)
(4) 6/pi
I found the length of the minor arc to be (pi)(r)/3 by doing a sixth of the circumference(2pi r).But I can't find the length of the radius to finish off the problem. If I knew the radius I would then plug it into the above and then use the radius again to be the length of the side because the triangle(one of the six of a hexagon) is equilateral. But can you show me how to get the radius to be 3? Thank you so much.
Answered by Walter Whiteley. 





A belt around two pulleys 
20041207 

From Ian: a belt is stretched around two pulleys whose centers are d units apart and whose radii are R and r respectively (obviously R+r<d). the challenge is to find the length of the belt, l as a formula in terms of R, r, and d only. Answered by Penny Nom. 





An arc of a circle 
20041205 

From Ruben: i have an arc 55 inches wide, 12 inches high at the centerline of the arc. how can i determine the diameter of the circle that would correspond to the arc. Answered by Penny Nom. 





Largest square inside a circle 
20041025 

From Bob: my granddaughter asked
what is the largest size square in inches
would fit in a 60 inch circle?
I believe it to be around 42.3 inches but
would like to teach her how to do it mathematically. Answered by Penny Nom. 





Perimeter and area of a semi_circle 
20040918 

From A student: I want to know how to find the perimeter and area of a semicircle and a quartercircle. Answered by Penny Nom. 





The radius of a circle 
20040824 

From Peter: If you slice any circle with a line, and call the distance of the line between intersections the "y" length and the perpendicular length to the shorter side of the curve the "x" length, what is the resulting equation for the radius? Answered by Penny Nom. 





The railing around a pool 
20040726 

From Bob: I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun. Answered by Penny Nom. 





The circle through three points 
20040706 

From Jim: I am a student trying to solve math problem. I'd like to calculate the radius of the circle that exactly fits any three points. If the points are (X1,Y1), (X2,Y2), and (X3,Y3), what is the radius of the circle that contains those three points? Answered by Penny Nom. 





The center of a circle 
20040526 

From Wan: I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency.
left side * right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius? Answered by Penny Nom. 





Circles in a hexagon 
20040411 

From Crystal: step by step can you show me how to calculate the area of the region inside the hexagon but outside the seven circles. given the radius of each circle is one inch Answered by Penny Nom. 





Numbers around a circle 
20040328 

From Rebecca: my maths question is use the numbers 1,2,3,4,5,6 and 7 place each number in a circle so each line adds up to 12. There are seven circles, six on the outside and one in the middle. Each number lines up with the middle number and the outside numbers line up with the one directly across from it as if a line was going through the middle number circle. Answered by Penny Nom. 





The radius of a circle 
20040306 

From A student: what is the radius of a circle with the circumference of 12 inches? Answered by Penny Nom. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





Areas, perimeters and derivatives 
20040215 

From Geoff: A recent lecture in my calculus class led me to realize that the derivative of the area of a circle, with respect to the radius is equal to the circumfrence. This also holds true for the relationship between the volume of a sphere and the surface area of that sphere:
why do these hold true? why is it only for circular objects? Answered by Harley Weston. 





An arc on a train track 
20040215 

From A student: I'm trying to build a route in a train simulator program. I have a curve to the right (an arc, in other words) with a length of 25 meters and the radius is 1,500 meters. Let's say point P is the beginning of the curve (arc) and point Q is the end point of the arc. Then picture a tangent to point P. I need to find the length of a line perpendicular to that tangent that runs to point Q (the end of the curve/arc). Answered by Penny Nom. 





The sides of a circle 
20040107 

From Helena: My name is Helena and I am 10 years old. On a resent math exam I was asked
the question" How many sides does a circle have?" and I wrote down none. The
teacher said the answer was one side. Answered by Chris Fisher. 





A locus 
20031202 

From Tash:
Question:
a)Find the equation of the locus of the point P which moves so that its distance from A(1,2) is always three times its distance from B(5,6)
b) Show that this locus is a circle and states the coordinates of its centre and the length of its radius
Answered by Penny Nom. 





The length of a chord 
20031103 

From David: When Radius=400.00' and Arc=130.58' what is the Cord distance in feet? Answered by Penny Nom. 





A circle around an irregular polygon 
20031103 

From Dale: How do I find the properties of a circle that is drawn around an irregular polygon of (n) sides with the lenghts of each side given and all end points of the polygon lye on the circumferance of the circle? Answered by Chris Fisher. 





Two chords 
20031007 

From Lori: Chords AB and CD of circle O intersect at E. If AE=4, AB=5, CE=2, Find ED. Answered by Penny Nom. 





The general equation for a sphere 
20030911 

From Jaidev: Is there any general equation for a sphere? Answered by Penny Nom. 





A theorem in geometry 
20030902 

From Diego: Please refer to figure in attached file. P is a point on the chord AB of a circle such that the tangent PT which touches the circle at T is equal to AB. How do we prove that PT^{2} = AP x BP. Answered by Dieter Ruoff and Penny Nom. 





A geometry problem 
20030708 

From Chris: My name is Chris, I work for a custom fabricator company. I am needing a formula for the Height (H) shown in the attached picture. The picture shows dimensions for my current application. If you could please, assign variables to the dimensions. Answered by Harley Weston. 





Definitions and descriptions 
20030608 

From Tammy: MY DAUGHTERS TEACHER ASKED HER TO GIVE BOTH A DESCRIPTION AND A DEFINITION OF THE FOLLOWING ... CIRCLE, SQUARE, TRIANGLE,HEXAGON...... THE LIST GOES ON. WHAT IS THE DIFFERENCE BETWEEN DEFINITION AND DESCRIPTION ? DO A CIRCLE FOR AN EXAMPLE PLEASE. Answered by Penny Nom. 





Circumference 
20030509 

From A parent: Find the circumference use 3 1/7 for pi
1. r= 28 ft. 2. D=98 cm Answered by Penny Nom. 





A circle, tangent to two circles and a line 
20030430 

From Keith: I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (XAxis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three. Answered by Chris Fisher and Harley Weston. 





A tangent to a circle 
20030418 

From Lech: The line with equation y=mx is a tangent to the circle with equation x2+y26x6y+17=0. Find the possible values of m. Answered by Harley Weston. 





Divide a circle in 8 equal pieces 
20030404 

From Naomi: I have to divide a circle in 8 equal pieces but can only cut 3 times can you please help me Answered by Penny Nom. 





A triangle and a circle 
20030321 

From Jynks: We need a formula that we can use to figure this out for work. We aren't math wiz's or students. Basically we know 3 points in space of a triangle, we know the length of each side and the length of the line from apex to base line. Each point of the base line ends upon the circumference of a circle. IS three a way to work out the radius of that circle. Answered by Penny Nom. 





An arc of a circle 
20030312 

From Melissa: A strip of wood is 16 ft. long and is bent in the arc of a circle. Two radii, from the center of the circle to the ends of the arc, form a right angle. What is the approximate distance from one end of the wooden arc to the other? Answered by Penny Nom. 





I have three circles... 
20030130 

From Tony: I HAVE THREE CIRCLE THAT IS CIRCLE TOGETHER: IN CIRCLE A, THE NUMBERS ARE: 11 I KNOW IS IN CIRCLE A, BUT I HAVE THE: 5 THAT IN A AND C, I HAVE THE 2 IN THE CIRCLE C AND B AND AND A, THE CIRCLE C I KNOW THAT 10 IS IN THE CIRCLE THE 4 IN CIRCLE A: AND B: IN CIRCLE B, I KNOW NUMBER 13 IS IN CIRCLE B; BUT I HAVE THE 3 IN CIRCLE B AND C AND I HAVE THE 2 IN CIRCLE B AND C AND A ,THE 4 IN CIRCLE B AND A. HOW DO I FIND THE SUM IN CIRCLE C AND IN B IN BOTH CIRCLE A AND B AND B AND C NOT IN CIRCLE B, AND NOT CIRCLE C. Answered by Penny Nom. 





Constructing a tangent to two circles 
20021128 

From Tom: I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles? Answered by Chris Fisher and Penny Nom. 





Subdividing a circle 
20021111 

From David: Say you have a cirlcle. Then you draw 2 dots on the circle. Then you connect the dots with lines. The circle is divided into 2 parts. If you do the same with 3 dots and connect each dot to each dot with a line then you get a circle with 4 parts. 4 dots with lines connecting all (6 lines) = 8 parts.... Answered by Claude Tardif. 





A Circle is evenly divided into six equal triangles 
20020916 

From Marilynn: A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Answered by Paul Betts. 





What really is pi? 
20020905 

From Rachel: what really is pi? 3.1444 Answered by Penny Nom. 





The circumference of a 72 
20020814 

From Linda: What is the circumference of a 72" diameter circle? Answered by Penny Nom. 





The area of a circle 
20020603 

From Jessica: I am doing a maths assigment for university, which is aimed towrds primary school students(k6). I was wondering if you could give me some information as to how I could describe to students the rule for finding the area of circle, using a circle cut up into equal sectors (like a pizza). I know it has something to do with the fact that you can make these shapes into a parallelogram, but I am a bit uncertain as to how I can express this idea clearly and articulately to students. Answered by Penny Nom. 





Overlapping circles 
20020529 

From Naman: There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^{ 2} (half the area of the small circle) If r=1, find the Radius of the big circle (R)? Answered by Harley Weston. 





3 radians subtends an arc of 27 meters 
20020522 

From Kyle: In circle O, a central angle of 3 radians intercepts an arc of 27 meters. Find the number of meters in the length of the radius. Answered by Penny Nom. 





Chord length 
20020517 

From Ashlie: How do you find the chord length of one section of a chord if you only have the diameter length and the other whole chord length. WV is the diameter and equals 16. XY is perpendicular to it, and equals 10. They intersect at pt. Z. I need to know what WZ equals. Please help! Answered by Penny Nom. 





A triangle in a circle of radius 6 
20020326 

From Marko: In a circle of radius 6, a triangle PQR is drawn having QR = 8 and PQ = 10. Determine the length of PR Answered by Chris Fisher. 





The isosceles triangle of smallest area 
20020308 

From Lettie: can you find the isosceles triangle of smallest area that circumscribes a circle of radius of one? Answered by Walter Whiteley. 





A circular wading pool 
20020304 

From Patrick: The community of melfort is planning to build a circular wading pool in the park. The pool will cover an area of 1000m^{2}. The building committee has decided to put a 5m cement pad around it. How much additional area will the cement pad take up? Answered by Harley Weston. 





Two circles inscribed in a rectangle 
20020227 

From Amina: Given a rectangle with dimensions L=6, H=5. Two circles are inscribed such that they touch each other(circles are adjacent to each other) and also their circumferences touch 2 sides of the rectangle. One of the circles has radius=4. Find the radius of the other circle. Answered by Penny Nom. 





The distance across a circle 
20020118 

From Douglas: If you know how far around a circle is (say earth) 25000 miles how do you calculate the distance across? Answered by Penny Nom. 





An octagon inscribed in a circle 
20020110 

From Kent: A circle of 30 in. diameter has an octagon (8 equal chords) inscribed in it. What is the length of each chord? Answered by Chris Fisher. 





Isoperimetric quotients 
20020102 

From A student: I'm stuck on my GCSE Maths coursework, what do isoperimetric quotients measure? Answered by Penny Nom. 





A circle and triangle overlap 
20011109 

From Tara: A circle and triangle overlap as shown.the area of the circle is three times the area of the triangle.If the common region is removed,then the area of the rest of the circle would be 14 sq cm more than the area of the rest of the triangle.How many sq cm are in the area of the complete triangle. Answered by Penny Nom. 





A circle and a triangle 
20011109 

From Tasha: I have a circle that has an equalateral triangle inscribed in it. The tip of the triangle (B) is at the center of the circle with the other corners (A & C) extending to the sides of the circle. I need to know the equation to find the linear length of AC. I also need to find the cordial length of the circle from point C to A. Answered by Penny Nom. 





Squaring the circle 
20011023 

From Margaret: I have the following question that I cannot answer on my own (I don't know where to begin): Is it possible construct a square whose area will equal the area of a given circle? Please Explain why or why not. Answered by Penny Nom. 





Dividing a circle 
20011017 

From Ahmeen: I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts. Answered by Walter Whiteley. 





A circle and a triangle 
20011004 

From Christina: The points (3,4), (9.2), and (3,2) define a circle and a triangle.  find the areas of the circle and the triangle. Find the difference between their areas.
 Find the length of a side of a square with the same area as the triangle.
 Find the length of a side of a Square with the same are as the circle.
Answered by Penny Nom. 





An egg shaped island 
20010922 

From Karen: I am a civil engineering designer trying to design an egg shaped island. I want a 30' radius at the top and a 40' radius at the bottom and the longest length of the egg to be 125'. Is there standard geometry for an egg shape? I am not held to exact radii or the length given. Answered by Chris Fisher. 





Three chords 
20010628 

From Paul: AE is a diameter of a circle and AC, CD and DE are chords of lengths 1, 2 and 3 respectively. (See the diagram.) Find the ridius of the circle. Answered by Harley Weston. 





Three tangents to a circle 
20010627 

From Stephanie: The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency. Prove that the perimeter of triangle PQR is equal to 2PT. Answered by Chris Fisher. 





How many sides does a circle have? 
20010516 

From Georganne: How many sides does a circle have? My son answered "infinate" on a test and was corrected. The school insists the answer is 0. Answered by Chris Fisher and Denis Hanson. 





Circles, ellipses, parabolas and hyperbolas 
20010509 

From Colleen: How is an ellipse like a circle? In what way does an ellipse have a center? How is a hyperbola similar and different to an ellipse? How is a parabola similar a different to a circle ellipse and parabola? Answered by Pnny Nom. 





A geometry proof 
20010418 

From Melissa: Extend the bisectors of angle A, angle B, and angle C of triangle ABC to meet the circumcircle at points X, Y, and Z respectively. Show that I is the orthocenter of triangle XYZ. Answered by Chris Fisher. 





The unit circle and trigonometry 
20010405 

From Ashley: "My teacher wants us to find out what a unit circle is, which I found out, a circle with the radius of 1, but the problem is he wants us to show the relationship between the unit circle and the sine(30,45,60 degrees), cosine(30,45,60 degrees),and tangent ratios(30,45,60 degrees). I need help with this and my teacher will not help us out. Thanks very much ... Answered by Penny Nom. 





Arc of a sphere 
20010304 

From Some students: My friends and i have a geometry project and we cannot seem to figure out how to find the arc of a sphere. Answered by Harley Weston. 





A quartercircle and two semicircles 
20001231 

From Christopher: Inside the quartercircle are two semicircles with the same radius, (r). Which has a greater area, G or L? Answered by Penny Nom. 





Inscribing a circle in a rhombus 
20001116 

From Jacky: A rhombus ABCD is drawn in which the diagonals are 12 and 20 units long. A circle is inscribed in the quadrilateral with the centre of the circle right on the intersection point of the 2 diagonals. The circumference of the circle touches all 4 sides of the rhombus. Is it possible to find the radius of the inscribed circle? If so, how and what is it? Answered by Chris Fisher. 





Overlapping a circle and a square 
20001028 

From Jacky: A square with a dimension 20 by 20cm. and a quarter of the circle with the radius of 25cm (A quater of a circle is created by 2 cuts that are perpendicular bisectors of each other where the intersecting point is at the centre of the circle). With these 2 pieces, the 2 pieces are placed over each other in which the 90^{o} angle of the quarter circle matches with one of the right angles on the square. Now, calculate the overlapping area of the 2 figures. Answered by Chris Fisher and Harley Weston. 





A chord length 
20001017 

From Al Paas: How to determine the length of a chord given the diameter of the circle and the maximum distance from the chord to The circle? Answered by Chris Fisher. 





Area of a circle 
20000803 

From Larry: I know the formula is pi r squared. For a circle 4 inches in diameter, do I multiply pi (3.1416) by the radius (2") then square the answer to that ie: 3.1416 X 2 squared or do I square the radius (2 X 2") then multiply by pi (3.1416) ?? Answered by Penny Nom. 





The circumference of a circle 
20000730 

From Not a student: An equalateral triangle is enclosed in a circle. The three corners touch the edges of the circle. One side of the triangle is 12. What is the circumference of the circle? Answered by Penny Nom. 





A semicircle and a triangle 
20000728 

From Ben: A semicircle and an isosceles triangle ABC have the same base AB and the same area. The equal angles in the triangle are BAC and CAB. I have to find the value of each of these angles. Answered by Harley Weston. 





Parallel tangents 
20000630 

From Ebony Indalecio: I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel. Answered by Walter Whiteley. 





Circumference = Area 
20000419 

From Scot George: The area and circumference of a circle has the same measurement. Find the radius. Answered by Chris Fisher. 





An equilateral triangle in a circle 
20000311 

From Michael Setlik: An equilateral triangle is drawn within a circle such that all three points of the triangle just touch the inside of the circle. Given the diameter of the cicle as six inches what is the length of the sides of the triangle? Answered by Harley Weston. 





Grazing area for a goat 
20000310 

From Amy: A goat is tied in the middle of a side of a square building whose sides are 2 yards long. The rope is 4 yards long. What is the grazing area for the goat? Answered by Harley Weston. 





Area of a circle 
20000229 

From Michelle Buboltz: My name is michelle and I just need to convert 25 ft across a circle into how many square feet. Answered by Penny Nom. 





The isoperimetric theorem 
20000224 

From Raj Bobal: How can you prove Mathematically that the maximum area enclosed by a given length is a circle? Answered by Chris Fisher. 





A triangle and a circle 
20000223 

From wendy: If a triangle of base 6 has the same area as a circle of radius 6, what is the altitude of the triangle? I am having trouble with altitude. Answered by Penny Nom. 





Filbert Family Circus 
20000204 

From Sarah: As Clyde moves his broom around the circus ring, he thinks that he has finally found a job where he can make a clean sweep of things. Clyde is sweeping the ring where the lions perform in the Filbert Family Circus. The ring is 76 feet across and Clyde is using a broom 3 feet wide. He starts at the outside edge and works his way to the middle, making circles around the ring. After sweeping 3/4 of the ring, Clyde sees the lions coming with their trainer and scurries out of the ring. How many trips around the ring did he make? Answered by Penny Nom. 





A problem with a radius. 
20000201 

From Howard B Davis: We start a Line that goes up 1 unit, then it goes to the Right for 5 units long, and then goes down 1 unit which is the end point. If we draw a circle that is tangent to both ends as well as the midpoint of the horizontal line: How do we find the radius of the arc; in Mathematics, with only this information? Answered by Chris Fisher. 





Arclength of a circle 
20000119 

From Holly: What is the formoula for finding the arc length of a central angle of a circle?? Answered by Harley Weston. 





Area of a circle and an inequality 
19991030 

From Adam Anderson: I have two problems. The first: prove that the area of a cirlce is pi times radius squared without using calculus. The second: show that ln(x) < x  1 for all x > 0. Answered by Harley Weston.






The circumference of a circle 
19991005 

From Mara Frost: what is the formula to find the circumference of a circle, or if there is no formula, how do you find the circumference of a circle? Answered by Penny Nom. 





Rolling Circles 
19990912 

From Craig Ellis: We have a circle of radius 3. inside the circle and tangent to the circle of radius 3 at one point is a circleof radius 1. The question is if we could roll the smaller circle around the inside of the larger circle how many revolutions would it take to get around to where we started. Answered by Chris Fisher and Walter Whiteley. 





Circles, cirmcuference and area 
19990516 

From Stephen Ehrler: I would appreciate if you could please tell me if what I discovered here is something or my ignorance? I noticed that a circle with r radii has the folling characteristic. r = [2 * ( pi * r^{2} / pi * 2r)] The equation states that the ratio of a circles area over its circumfrence = 1/2 that of the circles radii. It works every time. Did you know this ? Is it some kind of therom and can it be used for any thing? I thought this was intresting and would appreciate any input you may have. Thank you. Answered by Chris Fisher. 





Radius of an arc 
19990422 

From Rusty Riddleberger: I need to find the equation for finding the radius of an arc; I know the length of the arc (i.e the distance of the line connecting the two ends of the arc) and the height; (i.e the rise of the arc at its apex,) I had the formula years ago but it has lost me; this would be invaluable for work in new homes i.e. where we need to build an "arch" with a rise of 21" between two columns 11 feet apart Answered by Chris Fisher. 





Circles 
19990421 

From Alex Elkins: How do you find the circumference of a circle if you only know the radius and the square feet or inches of the circle if the radius is 18 inches, If done in inches do you multiply by 12 to get the square feet? Answered by Jack Lesage and Harley Weston. 





Volume of oil in a tank 
19990417 

From Lars Waldemarsson: My problem is to get an equation for the depth of the oil in a gastank formed like a cylinder. The cylinder is in a horizontal position and by a stick you will be able to get the depth of the oil in the tank. All I need is an exmaple which I can build on. By this equation you will be able to get the volume of the oil if you know the depth. Answered by Harley Weston. 





Dividing a Circle 
19990412 

From Mike Kenedy: I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example  1 line divides the circle into 2.
 2 into 4.
 3, however into 7.
 4 into11
 5 into 16
 6 into 22
 7 into 29
 8 into 37
 etc...
I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Answered by Penny Nom. 





Circumference and Area 
19990216 

From Natalie: finding the circumference of a circle? formula finding the area of a parallelogram? formula
Answered by Penny Nom. 





Dig digs in the garden 
19990211 

From Katherine Shaw: A circular garden has an a radius of 8m. Dig, the dog, is tied up to a fence that runs round the outside of the garden. Dig was able to dig up all the garden, apart from an area of 64 square metres, which he couldn't reach. How long was his lead? Answered by Chris Fisher and Harley Weston. 





Two Chords 
19980929 

From Jennifer Cane: Question: two parallel chords of a circle, AB and CD, have lengths of 10 cm and 17 cm respectively. The diameter of the circle is 21 cm. Find the shortest distance between the chords. Answered by Harley Weston. 





The area and the circumference of a circle. 
19980827 

From Jason Wright: I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me! Answered by Walter Whiteley. 





Two Inscribed Trapezoids 
19980127 

From James: A hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to m/n, where m and n are relatively prime positive integers. Find m+n. Answered by Haragauri Gupta. 





A geometry problem 
19971120 

From Herman: When produced, two equal chords AB and CD of a circle meet at P in an angle of 24 degrees. If H is the midpoint of AB and K is the midpoint of CD, calculate the size of angle HKD. Answered by Penny Nom. 





Pi 
19971031 

From Ryan McKinnon: What Is Pi? Answered by Chris Fisher. 





A Geometry Problem 
19970918 

From Rebecca Henry: A circle is centered at the vertex of the right angle of an isosceles triangle. The cirlce passes through both trisection points of the hypotenuse of the triangle. If the length of a radius of the circle is 10, find the area of the triangle. Answered by Chris Fisher Harley Weston. 





The Length of a Chord. 
19970726 

From Nathan Arthur: Picture a 9 inch diameter circle. Inside that circle is a 6 inch diameter circle tangent to it. Then, tangent to both circles is a 3 inch diameter circle. So there are three circles, two smaller ones inside a big one, all of them just touching but not overlapping. Now picture a chord on the 9 inch circle that is created by making a line that is tangent to both the 6 and the 3 inch circles and extending it to the edge of the 9 inch circle. I need the length of that cord. Answered by Chris Fisher. 





The angle between two tangents. 
19970609 

From Felix Ho: Two tangents are drawn from the origin to the circle (x)(x)+(y)(y)4x6y+9=0. If the angle between the tangents is m, fine the value of tan(m). P.S. (x)(x)=square x Answered by Harley Weston. 





Area Between Two Sectors 
19970302 

From Rebecca Henry: Points A,B,C,D,E,F are equally spaced on a unit circle. Arc CGE has a center A. Find the number of square units of area in the shaded region. Answered by Walter Whiteley. 





Some Circle Questions. 
19970225 

From Staci Vawser: A circle with a radius of 10m is drawn. A chord is drawn across the circle. How is the area that is formed between the chord and the arc calculated? Answered by Harley Weston. 





Circular Permutations 
19970205 

From Ed Varjassy: I have an understanding of simple problems involving circular permutations but do not understand them when they start to have restrictions. Is there any advice you can give for these more complicated permutations. Answered by Penny Nom. 





Common Area of two sectors. 
19961106 

From Lynda Mow: How do I find the area common to two intersecting circles of radii 8 ft and 10 ft if their common chord is 10 ft long? Answered by Penny Nom. 





A tangent to a circle is perpendicular to the radius at the point of contact. 
19961022 

From Rita Leung: I wonder if there is any proof for this theorem  A tangent to a circle is perpendicular to the radius at the point of contact. If there is any proof for that, can you tell me please? Answered by Chris Fisher and Harley Weston. 





Why is a circle divided into 360 degrees? 
19960930 

From Kurtis Kredo: I was recently wondering why a circle has been divided in to 360 degrees. When I asked my physics teacher he could not think of an answer. His guess is that it probably has to do with people long ago using the base 6 number system. I have a small inkling that it has to do with easy conversion or usage with radians or grads. Answered by Chris Fisher. 





Area of an annulus 
19960404 

From Ryan Levering: What is the area of this annulus? Answered by Penny Nom. 





Problème de géométrie 
20050429 

From Christian: C un cercle de centre I et de rayon 3 cm.
SORT est un carré inscrit dans le cercle C
M est un point quelconque de C Calculer la somme des carrés des distances de M aux sommets du carré (MS2 + MO2 +MR2 + MT2)
Cette somme dépendelle de la position de M sur le cercle ? Answered by Claude Tardif. 

