Let ABC be an acute triangle. Let MA,MB and MC be the midpoints of sides BC,CA, respectively AB. Let MA′,MB′ and MC′ be the the midpoints of the arcs BC,CA and AB respectively of the circumscriberd circle of triangle ABC. Let PA be the intersection of the straight line MBMC and the perpendicular to MB′MC′ through A. Define PB and PC similarly. Show that the straight line MAPA,MBPB and MCPC intersect at one point. geometryconcurrencyconcurrentarc midpoint