







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. 





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. 





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 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 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 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 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 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 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. 





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. 





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. 





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. 





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 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. 





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. 

