In a triangle ABC , let P be a point on its circumscribed circle (on the arc AC that does not contain B). Let H,H1,H2 and H3 be the orthocenters of triangles ABC,BCP,ACP and ABP, respectively. Let L=PB∩AC and J=HH2∩H1H3. If M and N are the midpoints of JH and LP, respectively, prove that MN and JL intersect at their midpoint. geometrymidpointparallelogram