AMC 12 2008a Problem 13

Points $A$ and $B$ lie on a circle centered at $O$, and $\angle AOB = 60^\circ$. A second circle is internally tangent to the first and tangent to both $\overline{OA}$ and $\overline{OB}$. What is the ratio of the area of the smaller circle to that of the larger circle?

$\mathrm{(A)}\ \frac{1}{16} \mathrm{(B)}\ \frac{1}{9} \mathrm{(C)}\ \frac{1}{8} \mathrm{(D)}\ \frac{1}{6} \mathrm{(E)}\ \frac{1}{4}$