1998 AHSME Problem 16

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

\mathrm{(A) \ } \sqrt{\frac ab} \qquad \mathrm{(B) \ }\frac ab \qquad \mathrm{(C) \ } \frac{a^2}{b^2} \qquad \mathrm{(D) \ }\frac{a+b}{2b} \qquad \mathrm{(E) \ } \frac{a^2 + 2ab}{b^2 + 2ab}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.