2011 AMC 12B Problem 6

Two tangents to a circle are drawn from a point A. The points of contact B and C divide the circle into arcs with lengths in the ratio 2 : 3. What is the degree measure of \angle{BAC}?

\textbf{(A)}\ 24 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 36 \qquad \textbf{(D)}\ 48 \qquad \textbf{(E)}\ 60

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