2012 AMC 12A Question 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 $C_1?$