Online Geometry Problems

Online Geometry Problem 1051: Triangle, Square, Semicircle, Arc, Area. Level: High School, SAT Prep, College, Mathematics Education


The figure below shows a square ABCD with M midpoint of AB. Arc AC of center D intersects the semicircles of diameters AM and BC at E and F, respectively. If S is the area of region ABCD, and S1, S2, S3, and S4 are the areas of regions AEF, BFE, CEF, and DEF, respectively, prove that (1) S = 85S1 = 34S2; (2) S1 + S2 + S3 = S4.
Problem submitted by Kadir Latintas, Math teacher in Emirdag, Turkey.

Geometry problem: Triangle, Square, Semicircle, Arc, Area



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Last updated: Oct 30, 2014