Question 93
Let $ABCD$ be a convex quadrilateral. $E$ and $F$ are points on the diagonal $AC$ such that $E$ and $F$ are interior points of triangles $ABD$ and $BCD$ respectively. Suppose $BE$ extend cuts $AD$ at $P$, $DE$ extend cuts $AB$ at $Q$, $DF$ extend cuts $BC$ at $R$ and $BF$ extend cuts $DC$ at $S$. Show that the three lines $QP$, $BD$ and $RS$ are either parallel or concurrent.