TUYMAADA 2017 S7

A point $E$ lies on the extension of the side $AD$ of the rectangle $ABCD$ over $D$ . The ray $EC$ meets the circumcircle $\omega$ of $ABE$ at the point $F\ne E$ . The rays $DC$ and $AF$ meet at $P$ . $H$ is the foot of the perpendicular drawn from $C$ to the line $\ell$ going through $E$ and parallel to $AF$ . Prove that the line $PH$ is tangent to $\omega$ .

(A. Kuznetsov)