BALTIC-WAY 2013 Problem 12

A trapezoid $A B C D$ with bases $A B$ and $C D$ is such that the circumcircle of the triangle $B C D$ intersects the line $A D$ in a point $E$, distinct from $A$ and $D$. Prove that the circumcircle of the triangle $A B E$ is tangent to the line $B C$.