Question 78
Let $ABCD$ be a trapezium with $AB \parallel CD$. Let $P$ be a point on $AC$ such that $C$ is between $A$ and $P$; and let $X$, $Y$ be the mid-points of $AB$, $CD$ respectively. Let $PX$ intersect $BC$ in $N$ and $PY$ intersect $AD$ in $M$. Prove that $MN \parallel AB$.