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 S_{1}, S_{2}, S_{3} , S_{4},
and S_{5} are the shaded areas, prove that: S_{1}
+ S_{2} + S_{3} = S_{4} + S_{5}.
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