KöMaL 2020 B5075

The midpoints of sides $AD$ and $BC$ of a convex quadrilateral $ABCD$ are $E$ and $F$, respectively. Line segment $EF$ intersects diagonal $AC$ at point $P$, and diagonal $BD$ at point $Q$. Prove that the circles $AEP$ and $BFQ$ intersect each other on the line $AB$.