Points A and B lie on a circle centered at O, and \angle A O B=60^{\circ}. A second circle is internally tangent to the first and tangent to both \overline{O A} and \overline{O B}. What is the ratio of the area of the smaller circle to that of the larger circle?
Answer Choices
A. \dfrac{1}{16}
B. \dfrac{1}{9}
C. \dfrac{1}{8}
D. \dfrac{1}{6}
E. \dfrac{1}{4}