Question 23
A cyclic quadrilateral $ ABCD $ is given. The lines $ AD $ and $ BC $ intersect at $ E $, with $ C $ between $ B $ and $ E $; the diagonals $ AC $ and $ BD $ intersect at $ F $. Let $ M $ be the midpoint of the side $ CD $, and let $ N \neq M $ be a point on the circumcircle of the triangle $ ABM $ such that $ AN/BN = AM/BM $. Prove that the points $ E, F $, and $ N $ are collinear.