2014 AMC 12A 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\qquad \textbf{(B) }1+\sqrt3\qquad \textbf{(C) }3\qquad \textbf{(D) }2+\sqrt3\qquad \textbf{(E) }4\qquad

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