Problem 100. Circle Area, Archimedes' Book of Lemmas. High School, College

In the diagram 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:


1. See: Archimedes' Book of Lemmas
   
Proposition 4
Arbelos

 

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Home | Geometry | Search | Problems | Areas | Art | Similarity | Circles | Semicircle | Lunes of Hippocrates | All Problems | 91-100 | Visual Index | Circle Tangent Line | Email | View or post a solution | by Antonio Gutierrez