AMC 12 2011b 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 \textbf{(B)}\ 30 \textbf{(C)}\ 36 \textbf{(D)}\ 48 \textbf{(E)}\ 60