Lesson 4: Let ABC be a triangle. The three altitudes AD, BE, CF intersect at H. let I, J,K be the midpoints of HA, HB, HC respectively. Let M, N, P be the midpoints of AB, BC and CA respectively. Prove that: a) Four points M, P, K, J are on the same circle
B) Six points M, P, K, J, I, N are on the same circle
c) Nine points M, P, K, J, I, N, D, E, F are on the same circle