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. r_{1},
and r_{2}, 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
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 illstructured 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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