A circle passing through the vertices $A$ and $B$ of a cyclic quadrilateral $ABCD$ intersects diagonals $AC$ and $BD$ at $E$ and $F$, respectively. The lines $AF$ and $BC$ meet at a point $P$, and the lines $BE$ and $AD$ meet at a point $Q$. Prove that $PQ$ is parallel to $CD$.
Dear Mathlinkers,
1. let P', Q' the second points of inersection of BF, CE with the circumcircle of ABCD.
2. Accordinf to Reim's theorem, CCD, EF and P'Q' are parallels.
3. According to Pascal's theorem, we are done.
Sincerely
Jean-Louis