2003 Pascal Problem 22

In the diagram, two circles with centres A and B intersect at points P and Q so that \angle PAQ = 60^\circ and \angle PBQ = 90^\circ. What is the ratio of the area of the circle with centre A to the area of the circle with centre B?

\textbf{(A)}\ 3:1\quad \textbf{(B)}\ 3:2\quad \textbf{(C)}\ 4:3\quad \textbf{(D)}\ 2:1\quad \textbf{(E)}\ 9:4

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Full credit to this problem is given to the CEMC, you may view all Pascal contests here.