2010 AMC8 Problem 23

#1
Semicircles \(POQ\) and \(ROS\) pass through the center \(O\). What is the ratio of the combined areas of the two semicircles to the area of circle \(O\)?
23.png
\( \textbf{(A)}\ \frac{\sqrt 2}{4}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{\pi}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{\sqrt 2}{2} \)