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