AT-OEMO-REG 2004 Problem 3

Given is a convex quadrilateral $ABCD$ with $\angle ADC=\angle BCD>90^{\circ}$ . Let $E$ be the point of intersection of the line $AC$ with the parallel line to $AD$ through $B$ and $F$ be the point of intersection of the line $BD$ with the parallel line to $BC$ through $A$ . Show that $EF$ is parallel to $CD$