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circles

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The region between two concentric circles 2014-10-27
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.
A circle is divided into three sectors 2014-04-17
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 2014-04-08
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.
A circle which is tangent to two perpendicular lines 2014-03-09
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.
2 concentric circles 2013-11-27
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 2013-10-19
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 . Thank-you , Jim

Answered by Penny Nom.
Four tangent circles 2013-10-09
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.
Four circles 2013-05-29
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 2013-05-22
From Alexandra:
There are two overlapping circles. The two non-overlapping 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.
Two congruent circles in a rectangle 2012-10-20
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.
Two circle problems 2012-10-05
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 12x-5y=0

Answered by Penny Nom.
Four tangent circles 2012-10-04
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.
The distance between overlapping circles 2012-07-26
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 common chord to two circles 2012-04-22
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.
Two overlapping circles 2012-03-21
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 non-overlapped portion of the small circle?
Answered by Penny Nom.
Circles 2012-03-11
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.
Two circles 2012-02-08
From crisfe:
find the point where the common cord of the circles x2+y2=25, x2+y2-12x-6y+35=0 process there line centers. what point they intercepts?
Answered by Penny Nom.
A fountain 2012-01-24
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 2012-01-23
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.
An equilateral triangle and some circles 2012-01-10
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 circles 2011-12-04
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.
One central circle and three tangent circles 2011-10-16
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 2011-10-06
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.
Three tangent circles 2011-08-21
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 2011-08-19
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.
concentric circles 2011-07-06
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.
Three tangent circles 2011-05-01
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.
A family of circles 2011-03-01
From steffi:
Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 -4x-28=0 and x^2 +y^2 -4x-20+52=0; the member tangent to x=7.
Answered by Penny Nom.
Two tangent circles 2011-02-09
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.
Semicircles and the Pythagorean Theorem 2011-01-09
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.
Two overlapping circles 2010-08-04
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.
Four circles in a square 2010-06-04
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 circle inscribed in a square inscribed in a circle 2010-04-28
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.
Two overlapping circles 2010-04-12
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.
Two overlapping circles 2010-03-07
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.
Two overlapping circles 2009-11-19
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.
Concentric circles 2009-10-14
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 2009-10-02
From Brandon:
There is a quarter circle with a radius of 1. along one eged of it, there is a semi-circl with a diameter of 1, and its center is on the drawn line. there is another semi-circle 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 2009-09-20
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 circles--vertical, horizontal, and diagonal -- add up to 12. Each number can be used only once.
Answered by Stephen La Rocque.
Two circles 2009-08-03
From Karan:
We are given 2 circles with radii 12cm and 3 cm. We have to find AB
Answered by Penny Nom.
Two circles on a dome 2009-07-01
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.
Two tangent circles 2009-01-23
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 2009-01-23
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.
Three circles inscribed in a circle 2008-12-18
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.
Two tangent circles and common tangents 2008-12-01
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.
Four circles in a square 2008-11-19
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.
The region between two circles 2008-09-24
From Carol:
Good day! Here is a picture of the problem that we need to solve. (I send the picture through e-mail.) 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.
Two tangent circles 2008-08-22
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.
Area of triangle formed by three tangent circles 2008-07-31
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.
Two circles 2008-06-10
From cey:
the diameter of the larger circle is 20cm, and the smaller 10cm. what is the shaded area??
Answered by Janice Cotcher.
Three mutually tangent circles 2008-06-04
From Jacob:
If three circles are mutually tangent, does that mean that the two tangent lines are perpendicular?
Answered by Chris Fisher.
Two overlapping circles 2008-04-26
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.
Two intersecting circles 2008-04-17
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 2008-04-13
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 common chord to two circles 2008-03-09
From shubha:
please help me out with this problem. find the length of the common chord of the intersecting circles x2+y2-4x-5=0 and x2+y2-2x+8y+9=0
Answered by Stephen La Rocque.
Two circles and a triangle 2008-03-07
From Adrian:
The vertices of a right-angled 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.
Two circles in a rectangle 2008-01-18
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.
Seven circles in a circle 2008-01-10
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.
Great circles 2007-11-05
From Lindsay:
Does a sphere have only ONE great circle? Explain?
Answered by Stephen La Rocque.
Three circles 2007-09-29
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.
Two circles C1 and C2 meet at the points A and B 2007-08-15
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.
A sequence of circles 2007-06-11
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.
Two concentric circles form an annulus 2007-05-02
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. 2007-04-21
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.
Two concentric circles 2007-04-19
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 semi-circles are drawn inside a square 2007-04-19
From James:
Four semi-circles 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.
Area of circles within a circle 2007-04-08
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.
circles 2007-03-06
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.
Circles 2007-02-22
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.
Two concentric circles 2007-02-11
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.
Circles and polygons 2006-12-11
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.
Sectors of a circle 2006-11-30
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.
Conic sections 2006-11-19
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.
An equilateral triangle has been wedged in between two circles. 2006-09-22
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.
Three circles inside a larger circle 2006-04-16
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 2006-04-15
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 2006-04-10
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 2006-04-07
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.
Make 2 rows of 4 circles with only 6 circles 2006-01-31
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 2006-01-25
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 sequence of circles and tangents 2006-01-16
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.
Four tangent circles 2005-12-06
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.
Framing an arched wall 2005-08-12
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 overlapping circles 2005-03-20
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.
Three tangent circles 2005-01-25
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.
Arcs and chords 2005-01-09
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.
Irrigation and a sector of a circle 2004-12-23
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. 2004-12-08
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 2004-12-07
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 2004-12-05
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.
Circles in a hexagon 2004-04-11
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.
A theorem in geometry 2003-09-02
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 PT2 = AP x BP.
Answered by Dieter Ruoff and Penny Nom.
Definitions and descriptions 2003-06-08
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.
A circle, tangent to two circles and a line 2003-04-30
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 (X-Axis) 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.
I have three circles... 2003-01-30
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 2002-11-28
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 2002-11-11
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 2002-09-16
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.
The circumference of a 72 2002-08-14
From Linda:
What is the circumference of a 72" diameter circle?
Answered by Penny Nom.
Overlapping circles 2002-05-29
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.
Chord length 2002-05-17
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.
Three chords 2001-06-28
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 2001-06-27
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.
Circles, ellipses, parabolas and hyperbolas 2001-05-09
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 quarter-circle and two semi-circles 2000-12-31
From Christopher:
Inside the quarter-circle are two semi-circles with the same radius, (r). Which has a greater area, G or L?
Answered by Penny Nom.
Grazing area for a goat 2000-03-10
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.
Rolling Circles 1999-09-12
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 1999-05-16
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 * r2 / 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.

Circles 1999-04-21
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.
Two Inscribed Trapezoids 1998-01-27
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 1997-11-20
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 mid-point of AB and K is the mid-point of CD, calculate the size of angle HKD.
Answered by Penny Nom.
The Length of a Chord. 1997-07-26
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.

Area Between Two Sectors 1997-03-02
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. 1997-02-25
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.
 
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