jmc

By the Pythagorean Theorem, the radius of the larger circle turns out to be $\sqrt{1^2+1^2}=\sqrt{2}$. Therefore, the area of the larger circle is $(\sqrt{2}{)}^2\pi =2\pi$. Using the coordinate plane given, we find that the radius of each of the two semicircles to be 1. So, the area of the two semicircles is $1^2\pi =\pi$. Finally, the ratio of the combined areas of the two semicircles to the area of circle $O$ is $\boxed{\frac{1}{2}}$.