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Semi-circle Lunes

Problem

A triangle is formed by connecting the two ends of the diameter of a semi-circle, length c, to a point on the circumference. Circles are constructed on the two shorter sides with diameters a and b respectively, so as to form two lunes (the shaded part).


Find the total area of the two lunes in terms of a, b, and c.

Problem ID: 173 (May 2004)     Difficulty: 2 Star

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