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In the diagram below, given a right
triangle ABC and semicircles of diameters AB, BC, AC, AO, OD,
and CD respectively. If OD is the perpendicular bisector of AC
and S, S1, S2, and S3 are the
shaded areas, prove that: S = S1 + S2 + S3.
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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."
1. See: :
The General Extension to Pythagoras' Theorem.
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