BALKAN-SL 2013 G3

Two circles $\Gamma_1$ and $\Gamma_2$ intersect at points $M,N$ . A line $\ell$ is tangent to $\Gamma_1 ,\Gamma_2$ at $A$ and $B$ , respectively. The lines passing through $A$ and $B$ and perpendicular to $\ell$ intersects $MN$ at $C$ and $D$ respectively. Prove that $ABCD$ is a parallelogram.