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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. 

Circumscribed pentagon, semiperimeter, tangent



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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