1998 AHSME Problem 16

Geometry Level 3

The figure shown is the union of a circle and two semicircles of diameters a and b, all of whose centers are collinear. The ratio of the area, of the shaded region to that of the unshaded region is

a b \frac{a}{b} a 2 + 2 a b b 2 + 2 a b \frac{a^2+2ab}{b^2+2ab} a + b 2 b \frac{a+b}{2b} a 2 b 2 \frac{a^2}{b^2}

Daniel Hirschberg by Daniel Hirschberg , 39, USA

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