







A triangle and an incircle 
20130509 

Max pose la question : 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. Chris Fisher lui répond. 





A triangle and an inscribed circle 
20080901 

Nancy pose la question : 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? Chris Fisher lui répond. 





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

Saurabh pose la question : Given an isosceles Triangle, whose one angle is 120 and inradius is √3. So area of triangle is? Stephen La Rocque lui répond. 





Discovering the incircle of an irregular polygon 
20070525 

Joaquim pose la question : 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? Walter Whiteley lui répond. 





A triangular prism 
20070326 

Tom pose la question : 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 Penny Nom lui répond. 





A geometry proof 
20010418 

Melissa pose la question : 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. Chris Fisher lui répond. 

