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 S_{1} 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 illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given." 