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 ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."