Problem 28 with Solution: Right Triangle, Altitude, Inradius, Tangency Points, Congruence, Measure. Level: High School, College, SAT Prep.

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In triangle ABC, angle B is a right angle. BD is the altitude. r₁, and r₂, are the inradii of the triangles ADB, and BDC respectively, the points E, F, and G are points of tangency. Prove that .