In a trapezoid ABCD with AB<CD and AB∥CD, the diagonals intersect each other at E. Let F be the midpoint of the arc BC (not containing the point E) of the circumcircle of the triangle EBC. The lines EF and BC intersect at G. The circumcircle of the triangle BFD intersects the ray [DA at H such that A∈[HD]. The circumcircle of the triangle AHB intersects the lines AC and BD at M and N, respectively. BM intersects GH at P, GN intersects AC at Q. Prove that the points P,Q,D are collinear. geometrytrapezoidcollinearity