# 2010 AMC8 Problem 23

#### bridge

##### Member
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 $$O$$?

$$\textbf{(A)}\ \frac{\sqrt 2}{4}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{\pi}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{\sqrt 2}{2}$$