Given a pointed triangle ABC with orthocenter H. Let D be the point such that the quadrilateral AHCD is parallelogram. Let p be the perpendicular to the direction AB through the midpoint A1 of the side BC. Denote the intersection of the lines p and AB with E, and the midpoint of the length A1E with F. The point where the parallel to the line BD through point A intersects p denote by G. Prove that the quadrilateral AFA1C is cyclic if and only if the lines BF passes through the midpoint of the length CG. geometryparallelogrambisectscyclic quadrilateralConcyclicbisects segment