Let ABC be an isosceles triangle with AB=AC. Let AD be the diameter of the circumcircle of ABC and let P be a point on the smaller arc BD. The line DP intersects the rays AB and AC at points M and N, respectively. The line AD intersects the lines BP and CP at points Q and R, respectively. Prove that the midpoint of MN lies on the circumcircle of PQR geometrymidpointcircumcircleisosceles