







The sides of a 5pointed star inscribed in a circle 
20210918 

From Scott: Is there a calculation for the length of each side of a fivepointed star?
I am not worried about area but if I have a circle with a 7.5 foot radius and
place a star inside it, how can I measure the lines creating the star? Answered by Harley Weston. 





A circle inscribed in a triangle 
20190428 

From Daksh: O is the centre of the inscribed circle in a 30°60°90° triangle ABC right angled at C.
If the circle is tangent to AB at D then the angle COD is Answered by Penny Nom. 





An equilateral triangle inscribed in a circle 
20190129 

From Penny: What is the length of each side of the largest equilateral triangle that fits inside a 3 inch diameter circle? Answered by Penny Nom. 





A circle inscribed in a regular polygon 
20180712 

From Naveen: The radius of inscribed circle for n sided regular polygon of a side a is?
Please with proof Answered by Penny Nom. 





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. 





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. 





Quadrilateral ABCD is inscribed in a circle 
20170911 

From Joie: Quadrilateral ABCD is inscribed in a circle such that side DA is the diameter. AB=2m., BC=4m., CD=6m., angle BAD=75.93degrees. Find the area of the quadrilateral. 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. 





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. 





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. 





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 cone inscribed in a hemisphere 
20160807 

From anonymous: A cone is inscribed in a hemisphere. the slant height of the cone is 20cm. When cut along its slant height, the cone forms a sector of a circle.
find the angle of the sector, to the nearest 1 decimal place. 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. 





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 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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





A cone inscribed in a sphere 
20140228 

From joel: how can I find the radius and the height of a cone INSCRIBED in a sphere, given the sphere having a radius of 6? ( note: the diameter of the cone is equal to its slanted height). Answered by Penny Nom. 





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. 





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. 





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. 





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. 





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. 





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 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 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. 





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 cube inscribed in a sphere 
20120123 

From Gelo: What are the largest volume and total surface area of a cube that may be inscribed inside a sphere whose radius is 5 kilometers. Answered by Walter Whiteley. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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 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. 





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. 





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. 





A pentagon inscribed in a circle 
20090729 

From Faisal: O is the center of the circle. Sides AB and AE are equal. Angle B = 95,
angle C = 130, angle D = 138. Find angles A and E.
Diagram is attached.
Best,
Faisal Answered by Chris Fisher. 





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. 





The volume of water in a cone 
20090317 

From Freddie: A ball of diameter 20cm rests in a conical container whose angle with the slant height and the vertical axis is 25degrees. if water is poured into the container just enough to touch the bottom of the ball, find the quantity of water in the container. 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 sphere in a cone 
20090210 

From Shubham: An upturned conical vessel of radius 6cm and height 8cm is completely
filled with water. A sphere is lowered in the conical vessel filled with
water and the size of sphere is such that it just touches the sides of
cone and is just immersed. What fraction of water overflows? Answered by Harley Weston. 





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. 





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. 





A triangle inscribed in a circle 
20081117 

From Wanda: I have the same question that you guys answered 20070302. I need more clarification. I UNDERSTAND how to get the radius=3, I get that it is an equilateral triangle so each vertex is 60 degrees, I get that area of triangle is 1/2 bh.
I DO NOT understand why we multiply area X 3 , or how to calculate the values of base and height. Please explain a little further. Thanks.
Wanda Answered by Penny Nom. 





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. 





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. 





A square is inscribed within a square 
20080719 

From Shirley: A square is inscribed within a square that has a side the measures 16
centimeters. The vertices of the smaller square are located at the midpoints
of the sides of the larger square. What is the area of the larger square, area of
a smaller square, the probability that a point chosen at random is in the
shaded are? Express the answer as a simplified fraction. Answered by Penny Nom. 





A cube inscribed in a right cone 
20080716 

From Steven: A cube is inscribe in a right cone of radius 2 and height 5. What is the volume of the cone? Answered by Victoria West and Harley Weston. 





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. 





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 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. 





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. 





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. 





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. 





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. 





Inscribed square in a triangle 
20080127 

From Adrian: Consider a rightangled triangle PQR, where QR is the base and PQ is the height.
QR=4cm and PQ=3cm. A square is inscribed in this triangle.Determine the length
of one side of the square. Answered by Stephen La Rocque. 





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. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





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. 





The area of an octagon inscribed in a circle 
20071201 

From Harry: I need to find the area of an octagon in a circle. each point of the octagon touches the edge of the circle, and the circle's diameter = 4 cm. What is the area of the octagon Answered by Penny Nom. 





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. 





Size of a sphere fitting inside a cone 
20070927 

From Juan: I am supposed to find the largest sphere that
will fit into a cone. I am assuming is a maximizing problem, but I am not sure
of what relation (between a cone and a sphere) to use. Answered by Penny Nom and Stephen La Rocque. 





A cube in a sphere 
20070911 

From Justin: What percent of the volume of a cube is occupied by the largest possible sphere centered in that cube? Answered by Stephen la Rocque. 





A rectangle inscribed in a circle 
20070911 

From Sobeida: A rectangle that is x feet wide is inscribed in a circle of radius 8 feet. What is the area of the rectangle as a function of x.
Thanks! Answered by Stephen la Rocque. 





Find the area of a regular pentagon inscribed in a circle 
20070803 

From Tracy: Can you please help me with finding the area of a regular pentagon inscribed in a circle using the Pythagorean theorem. The radius of the circle is 5 cm and each side AB = BC = CD = DE = EA = 6 cm. Answered by Stephen La Rocque, Leeanne Boehm and Chris Fisher. 





Area of a star in a regular pentagon with side length 10cm 
20070724 

From Chetna: A regular pentagon with side 10 cm has a star drawn within (the vertices match).
What is the area of the star? 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. 





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. 





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. 





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. 





The area of an inscribed triangle 
20070302 

From Caitlin: What is the area of an equalateral triangle inscribed in a circle whose circumference is 6 pie?? PLEASE HELP 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. 





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. 





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. 





An octagon inscribed in a square 
20061229 

From Richard: An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters. What is the number of square centimeters in the area of the octagon? Answered by Walter Whiteley. 





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. 





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 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. 





What is the diameter of the circle that contains this octagon? 
20060921 

From Dave: if the distance between two parallel sides of an octagon is 350 cm, what is the diameter of the circle that contains this octagon (ie. a circle that touches all eight corners)? Answered by Stephen La Rocque. 





A cube inscribed in a sphere 
20060803 

From Glenn: Given the diameter of the sphere 10cm. find the largest cube inscribe in the sphere. 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. 





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. 





A cube in a sphere 
20051019 

From Damian: A sphere passes through the eight corners of a cube side 10cm. Find the volume of the sphere. Answered by Penny Nom. 





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. 





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. 





A cube is inscribed inside a sphere 
20040818 

From A student: A cube is inscribed inside a sphere with radius sqrt8cm. Find the
(a) length of the cube
(b) volume of the space inside the sphere but outside the cube. 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. 





A rectangle in a circle 
20030927 

From Abdu: A rectangle ABCD is inscribed in a circle. If the length of AB is 5 and length of BC is 12, what is the area of circle outside the rectanlge ABCD? Answered by Penny Nom. 





A sphere inscribed in a cone 
20030810 

From A student: A sphere with radius 5cm is inscribed in a right circular cone 20 cm in height.find
(a) the base radius ,volume of the cone (b)volume of the shaded space( to 3 sig fig) Answered by Penny Nom. 





A polygon inscribed within an ellipse  Part 2 
20020708 

From Steven: I recently sought your advice about a problem that I have been working on for eight years or so concerning a polygon inscribed within an ellipse. I think that I may have confused matters by the way in which I put the question and hope that the enclosed diagram will clear matters up. In the ellipse below I have drawn three chords inscribed within one quadrant ( this would pertain to a twelve sided figure within the whole ellipse). These chords are exactly the same length as each other, for example if the major axis of the ellipse was 360 and the minor axis 240 I have worked out that a twelve sided figure would have sides of 78.2487. However I worked this out empirically with a method that could only be described as gruelling I would be most grateful if you could tell me of a method that would work for any ellipse and any number of sides. Answered by Chris Fisher. 





An equalateral polygon inscribed within an ellipse 
20020630 

From Steven: How would you calculate the length of one of the sides of an equalateral polygon (of n sides) inscribed within an ellipse ( of any eccentricity ) where all of the vertices exactly touch the perimeter of the ellipse? I know that when the eccentricity is zero ( i.e a circle ) the formula: r * (sin(180/n) * 2) will suffice. But what about when the eccentricity is greater than zero? Answered by Chris Fisher. 





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. 





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. 





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. 





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. 





A tetrahedron inscribed in a cube 
19981118 

From Jane: In analyzing a cube, I would like to find a tetrahedron inscribed in the cube which has none of its faces in the planes of the faces of the cube. I would like to see this tetrahedron outlined in the cube. My name is Jane and my email address is BARSOIAN. I am an elementary education student. 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. 

