2008 AMC 10A Problem 16

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.