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

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 .
 


 

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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