The Brocard axis is the line K O passing through the symmedian point K and circumcenter O of a triangle, where the segment O K is the Brocard diameter. The Brocard axis is perpendicular to the Lemoine axis and is the isogonal conjugate of the Kiepert hyperbola. It is central line L_523 and has equivalent trilinear equations sin(B - C) α + sin(C - A) β + sin(A - B) γ = 0 and b c(b^2 - c^2) α + c a(c^2 - a^2) β + a b(a^2 - b^2) γ = 0.

Brocard circle | Brocard diameter | Brocard line | Brocard triangles