2010 AMC 10B Problem 19

A circle with center O has area 156\pi. Triangle ABC is equilateral, \overline{BC} is a chord on the circle, OA = 4\sqrt{3}, and point O is outside \triangle ABC. What is the side length of \triangle ABC?

\textbf{(A)}\ 2\sqrt{3} \qquad \textbf{(B)}\ 6 \qquad \textbf{(C)}\ 4\sqrt{3} \qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 18

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