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.