Problem 22: Right triangle, Altitude, Perpendiculars, Inradii
Level: High School, SAT Prep, College geometry
The figure shows a right triangle ABC
with the altitude BD. Lines DE and DF are perpendicular to AB
and BC, respectively, r, r1, and r2 are
the inradii of the triangles ABC, AED, and DFC respectively.
Prove that r1 + r2 = r.