IT-CESENATICO 2005 Problem 6

Two circles $\gamma_1, \gamma_2$ in a plane, with centers $A$ and $B$ respectively, intersect at $C$ and $D$ . Suppose that the circumcircle of $ABC$ intersects $\gamma_1$ in $E$ and $\gamma_2$ in $F$ , where the arc $EF$ not containing $C$ lies outside $\gamma_1$ and $\gamma_2$ . Prove that this arc $EF$ is bisected by the line $CD$ .