Question 7
Let $ABCD$ be a convex quadrilateral inscribed in a circle $\omega$. The bisector of $\angle BAC$ meets $\omega$ at $E$ $(\ne A)$, the bisector of $\angle ABD$ meets $\omega$ at $F$ $(\ne B)$, $AE$ intersects $BF$ at $P$ and $CF$ intersects $DE$ at $Q$. Suppose $EF=20$, $PQ=11$. Find the area of the quadrilateral $PEQF$.