AHSME 1967 Problem 33

In this diagram semi-circles are constructed on diameters $\overline{AB}$, $\overline{AC}$, and $\overline{CB}$, so that they are mutually tangent. If $\overline{CD} \bot \overline{AB}$, then the ratio of the shaded area to the area of a circle with $\overline{CD}$ as radius is: $\textbf{(A)}\ 1:2 \textbf{(B)}\ 1:3 \textbf{(C)}\ \sqrt{3}:7 \textbf{(D)}\ 1:4 \textbf{(E)}\ \sqrt{2}:6$