Problem 95.
Similar Triangles, Inradii, Parallel.
Level: High School, SAT Prep, College

In the figure below, given a triangle
ABC, line DEF parallel to AC and line FGM parallel to AB. If r,
r_{1}, r_{2}, and r_{3}, are the inradii
of triangles ABC, DBE, FGE, and MGC respectively, prove that: r
= r_{1}
+ r_{2} + r_{3}.
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FACTS AND HINTS:

1. SIMILAR TRIANGLES:
Proposition:
Corresponding segments of similar triangles are in proportion.