Let Δ H_A H_B H_C be the orthic triangle of a triangle Δ A B C. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection lie on a line O_A O_B O_C called the orthic axis of Δ A B C. The orthic axis is central line L_3, has trilinear equation α cos A + β cos B + γ cos C = 0. It is perpendicular to the Euler line. It passes through Kimberling centers X_i for i = 230, 232, 468, 523 (isogonal conjugate of the focus of the Kiepert hyperbola), 647, 650, 676, 1637, 1886, 1990, 2485, 2489, 2490, 2491, 2492, 2493, 2501, 2506, 2977, 3003, 3011, 3012, and 3018. The anticomplement of the orthic axis is the de Longchamps line.

antiorthic axis | coaxal system | orthic triangle