Problem 27 Level: High School, SAT Prep, College
geometry

In triangle ABC,
angle B is a right angle. O is the incenter of triangle ABC,
From O parallels FG and HM are drawn to AB, and BC. r1,
and r2, are the inradii of the triangles AHM, and
FGC respectively, the points D and E are points of tangency. Prove that
.