KöMaL 2018 A729

In a cyclic quadrilateral $ABCD$, the diagonals meet at point $E$, the midpoint of side $AB$ is $F$, and the feet of perpendiculars from $E$ to the lines $DA$, $AB$, and $BC$ are $P$, $Q$, and $R$, respectively. Prove that the points $P$, $Q$, $R$, and $F$ are concyclic.