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, r_{1}, and r_{2} are
the inradii of the triangles ABC, AED, and DFC respectively.
Prove that r_{1} + r_{2} = r.
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