OMCPLP 2021 Problem 3

Let triangle $ABC$ be an acute triangle with $AB\neq AC$ . The bisector of $BC$ intersects the lines $AB$ and $AC$ at points $F$ and $E$ , respectively. The circumcircle of triangle $AEF$ has center $P$ and intersects the circumcircle of triangle $ABC$ at point $D$ with $D$ different to $A$ .

Prove that the line $PD$ is tangent to the circumcircle of triangle $ABC$ .