Let P be the intersection point of the diagonals of the quadrangle ABCD, M the intersection point of the lines connecting the midpoints of its opposite sides, O the intersection point of the perpendicular bisectors of the diagonals, H the intersection point of the lines connecting the orthocenters of the triangles APD and BCP, APB and CPD. Prove that M is the midpoint of OH. geometryorthocentermidpoint