Given a triangle ABC, let D be the midpoint of the side AC and let M be the point that divides the segment BD in the ratio 1/2; that is, MB/MD=1/2. The rays AM and CM meet the sides BC and AB at points E and F, respectively. Assume the two rays perpendicular: AM⊥CM. Show that the quadrangle AFED is cyclic if and only if the median from A in triangle ABC meets the line EF at a point situated on the circle ABC. geometrycircumcircleratiogeometry proposed