Problem 344. Quadrilateral, Extension of sides, Circle, Tangent,
Semiperimeter. Level: High School, College, SAT Prep.
The figure shows a quadrilateral ABCD.
The extension of the sides are tangent to circle O at E, F, G,
and H. If s is the semiperimeter of the quadrilateral, prove
that s = AB + BC = AD + CD.
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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