In the figure below, given an square
ABCD of area S, E is the intersection of BD and the semicircle
of diameter AD, and CF is tangent to the semicircle. If S1 is
the area of triangle DEF, prove that: .
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FACTS AND HINTS:
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."