Let A', B', C' the altitude feet; A”, B”, C” the midpoints of the sides. Let Ab, Ac, Bc, Ba, Ca, Cb be the circumcenters of A'BC”, A'B”C, B'CA”, B'C”A, C'AB”, C'A”B. The triangle ABC and the triangle bounded by BcCb, CaAc, AbBa are orthologic, with orthologic centers the centroid G and the point P in the Euler line dividing HN (H orthocenter, N ninecenter) in the ratio 1:2.