NZ-NZMO 2019 Problem 7

Let $ABCDEF$ be a convex hexagon containing a point $P$ in its interior such that $PABC$ and $PDEF$ are congruent rectangles with $PA = BC = PD = EF$ (and $AB = PC = DE = PF$ ). Let $\ell$ be the line through the midpoint of $AF$ and the circumcentre of $PCD$ . Prove that $\ell$ passes through $P$ .