Let A', B', C' be the altitude feet; A”, B”, C” the midpoints of AA', BB', CC'; A*, B*, C* the midpoints of AH, BH, CH (H orthocenter). Let Ga, Gb, Gc be the centroids of A*B”C”, B*C”A”, C*A”B”. The lines A'Ga, B'Gb, C'Gc concur.