This article is about triangles in which the lengths of the sides and the radii of the inscribed circles are all whole numbers.
One side of a triangle is divided into segments of length a and b
by the inscribed circle, with radius r. Prove that the area is:
The square ABCD is split into three triangles by the lines BP and
CP. Find the radii of the three inscribed circles to these
triangles as P moves on AD.
A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?