MA-MO 2005 Problem 1

In a square $ABCD$ let $F$ be the midpoint of $\left[ CD\right]$ and let $E$ be a point on $\left[ AB\right]$ such that $AE>EB$ . the parallel with $\left( DE\right)$ passing by $F$ meets the segment $\left[ BC\right]$ at $H$ . Prove that the line $\left( EH\right)$ is tangent to the circle circumscribed with $ABCD$