RMO 2013 M1

Let $ABC$ be an isosceles triangle with $AB=AC$ and let $\Gamma$ denote its circumcircle. A point $D$ is on arc $AB$ of $\Gamma$ not containing $C$ . A point $E$ is on arc $AC$ of $\Gamma$ not containing $B$ . If $AD=CE$ prove that $BE$ is parallel to $AD$ .