







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. 





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. 





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 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 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. 





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. 





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. 





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 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 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. 





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 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 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. 





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 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. 





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 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. 





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 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 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 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. 





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. 

