2010 AMC 10B Problem 20

Two circles lie outside regular hexagon ABCDEF. The first is tangent to \overline{AB}, and the second is tangent to \overline{DE}. Both are tangent to lines BC and FA. What is the ratio of the area of the second circle to that of the first circle?

\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 27 \qquad \textbf{(C)}\ 36 \qquad \textbf{(D)}\ 81 \qquad \textbf{(E)}\ 108

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