2012 AMC 12A Problem 16

Circle C_1 has its center O lying on circle C_2. The two circles meet at X and Y. Point Z in the exterior of C_1 lies on circle C_2 and XZ=13, OZ=11, and YZ=7. What is the radius of circle C_1?

\textbf{(A)}\ 5\qquad\textbf{(B)}\ \sqrt{26}\qquad\textbf{(C)}\ 3\sqrt{3}\qquad\textbf{(D)}\ 2\sqrt{7}\qquad\textbf{(E)}\ \sqrt{30}

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