The two circles Γ1 and Γ2 intersect at P and Q. The common tangent that's on the same side as P, intersects the circles at A and B,respectively. Let C be the second intersection with Γ2 of the tangent to Γ1 at P, and let D be the second intersection with Γ1 of the tangent to Γ2 at Q. Let E be the intersection of AP and BC, and let F be the intersection of BP and AD. Let M be the image of P under point reflection with respect to the midpoint of AB. Prove that AMBEQF is a cyclic hexagon. hexagonCyclicgeometrycircles