ILL 1977 Problem 55

Through a point $O$ on the diagonal $BD$ of a parallelogram $ABCD$ , segments $MN$ parallel to $AB$ , and $PQ$ parallel to $AD$ , are drawn, with $M$ on $AD$ , and $Q$ on $AB$ . Prove that diagonals $AO,BP,DN$ (extended if necessary) will be concurrent.