Let I be the incenter of △ABC and let Ha, Hb, and Hc be the orthocenters of △BIC , △CIA, and △AIB, respectively. The lines HaHb meets AB at X and the line HaHc meets AC at Y. If the midpoint T of the median AM of △ABC lies on XY, prove that the line HaT is perpendicular to BC geometryincenterorthocenter