Problem 341. Triangle, Inscribed circle, Tangent, Semiperimeter.
Level: High School, College, SAT Prep.
The figure shows a triangle ABC with
the inscribed circle I tangent to sides at D, E, and F. If s is
the semiperimeter of the triangle ABC, prove that s = AC + BE.
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 ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."