Problem 100. Circle Area, Archimedes' Book of Lemmas. Level: High School, SAT Prep, College

In the figure below, given a semicircle of diameter AB, CD is a perpendicular to AB, circle of diameter CD and semicircles of diameter AC and CB respectively. If S1, S2, S3 , S4, and S5 are the shaded areas, prove that: S1 + S2 + S3 = S4 + S5
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Circle Area, Archimedes Book of Lemmas 

 

 

 

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: Archimedes' Book of Lemmas
   
Proposition 4
Arbelos


 

Circle area, Elearning

 

 

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Last updated: May 22, 2009