Question 121
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 $P$.