Let ABC be a an acute triangle. Points A1,B1 and C1 are respectively the projections of the vertices A,B and C on the opposite sides of the triangle, the point H is the orthocenter of the triangle, and the point P is the middle of the segment [AH]. The lines BH and A1C1, PB1 and AB intersect respectively at the points M and N. Prove that the lines MN and BC are perpendicular. geometryperpendicularaltitudesorthocenter