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 $C_1$? $\textbf{(A)}\ 5\qquad$ $\textbf{(B)}\ \sqrt{26}\qquad$ $\textbf{(C)}\ 3\sqrt{3}\qquad$ $\textbf{(D)}\ 2\sqrt{7}\qquad$ $\textbf{(E)}\ \sqrt{30}$