Question 5
In trapezoid $ABCD$, none of whose interior angles is right, diagonals $AC,BD$ meet at $E$. Let $P,Q$ be the feet of the perpendiculars from $A,B$ to lines $BC,AD$, respectively. The circumcircles of triangles $CEQ,DEP$ meet again at $F\neq E$. Prove that lines $AP,BQ,EF$ are concurrent or parallel.