This just basically involves drawing it all out and using the facts that compose a 9 point circle. if you draw it out right, it should work
the feet of the altitudes decompose the nine-point circle into 3 arcs.Assume that the triangle is scalene.Prove that the remaining six of the nine points are distributed among the three arcs as follows: one arc contains just one of the six points, another contains two, and the third contains three