2008 AMC 12A Question 13 - thichhoctoan.com

Question 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 $OA$ and $OB.$ What is the ratio of the area of the smaller circle to that of the larger circle?

$\dfrac{1}{16}$
$\dfrac{1}{9}$
$\dfrac{1}{8}$
$\dfrac{1}{6}$
$\dfrac{1}{4}$