Question 52
$ABCD$ is a trapezium, in which a circle can be inscribed, with $AB$ parallel to $DC$ and $AD$ equal to but not parallel to $BC$. The inscribed circle touches $AB$, $BC$, $CD$ and $DA$ at $X$, $Y$, $Z$ and $W$ respectively. $XZ$ and $WY$ intersect at $P$. Prove that the diagonals of $ABCD$ pass through $P$.