Problem 99. Circle Area, General Extension to Pythagoras' Theorem. Level: High School, SAT Prep, College

In the figure 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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Circle Area problem. Elearning 99 

 

 

 

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.

Pythagoras_extension


 

Circle area and Pythagoras 

 

 

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Last updated: May 24, 2008