AMC 12 2014a Problem 12

Two circles intersect at points $A$ and $B$. The minor arcs $AB$ measure $30^\circ$ on one circle and $60^\circ$ on the other circle. What is the ratio of the area of the larger circle to the area of the smaller circle?

$\textbf{(A) }2 \textbf{(B) }1+\sqrt3 \textbf{(C) }3 \textbf{(D) }2+\sqrt3 \textbf{(E) }4$