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 S_{1}, S_{2}, S_{3}, and S_{4} are the areas of regions AEF, BFE, CEF, and
DEF, respectively, prove that (1) S = 85S_{1} = 34S_{2}; (2) S_{1} + S_{2} + S_{3} = S_{4}.
Problem submitted by Kadir Latintas, Math teacher in Emirdag, Turkey.
