## 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