BALKAN-SL 2015 G7

Let scalene triangle $ABC$ have orthocentre $H$ and circumcircle $\Gamma$ . $AH$ meets $\Gamma$ at $D$ distinct from $A$ . $BH$ and $CH$ meet $CA$ and $AB$ at $E$ and $F$ respectively, and $EF$ meets $BC$ at $P$ . The tangents to $\Gamma$ at $B$ and $C$ meet at $T$ . Show that $AP$ and $DT$ are concurrent on the circumcircle of $AFE$ .