SILK-ROAD 2012 Problem 1

Trapezium $ABCD$ , where $BC||AD$ , is inscribed in a circle, $E$ is midpoint of the arc $AD$ of this circle not containing point $C$ . Let $F$ be the foot of the perpendicular drawn from $E$ on the line tangent to the circle at the point $C$ . Prove that $BC=2CF$ .