Problem 342. Pentagon, Inscribed Circle, Tangent, Semiperimeter.
Level: High School, College, SAT Prep.
The figure shows a pentagon ABCDE with
the inscribed circle O tangent to sides at F, G, H, M, and N. If
s is the semiperimeter of the pentagon, prove that s = AB + CD +
EN = BC + DE + AN.
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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