Question 180
Let $P$ be a point of the intersection of diagonals of the cyclic quadrilateral $ABCD$. The circumscribed circles of $\triangle APD$ and $\triangle BPC$ intersect the line $AB$ at points $E$ and $F$ correspondingly. $Q$ and $R$ are projections of the point $P$ onto the lines $FC$ and $DE$. Prove that $AB \parallel QR$.