Let O be an inner point of an acute-angled triangle ABC. Let A1,B1 and C1 be the projections of O on the sides BC,AC and AB respectively . Let P be the intersection of the perpendiculars on B1C1 and A1C1 from pointsA and B respectilvey. Let H be the projection of P on AB. Show that points A1,B1,C1 and H lie on a circle. geometryConcyclicprojectionsprojection