AHSME 1973 Problem 15

A sector with acute central angle $\theta$ is cut from a circle of radius 6. The radius of the circle circumscribed about the sector is $\textbf{(A)}\ 3\cos\theta \textbf{(B)}\ 3\sec\theta \textbf{(C)}\ 3 \cos \frac12 \theta \textbf{(D)}\ 3 \sec \frac12 \theta \textbf{(E)}\ 3$