Problem 68.
Triangle, Incircle, Inradius, Tangent.
Level: High School, SAT Prep, College

In the figure below, r is the inradius
of a triangle ABC, d is the radius of circles D and E
tangent to the angles A and C respectively, and m = AF + CG.
Prove that: \(r = \dfrac{b \cdot d}{m}\).