Mock AIME 1 2006-2007 Problems/Problem 10
In , , , and have lengths , , and , respectively. Let the incircle, circle , of touch , , and at , , and , respectively. Construct three circles, , , and , externally tangent to the other two and circles , , and are internally tangent to the circle at , , and , respectively. Let circles , , , and have radii , , , and , respectively. If where and are positive integers, find .
Radius , radius , radius and , see picture.
Given , so .