A Brocard line is a line from any of the vertices A_i of a triangle Δ A_1 A_2 A_3 to the first Ω or second Ω' Brocard point. Let the angle at a vertex A_i also be denoted A_i, and denote the intersections of A_1 Ω and A_1 Ω' with A_2 A_3 as W_1 and W_2. Then the angles involving these points are ∠A_1 Ω W_3 | = | A_1 ∠W_3 Ω A_2 | = | A_3 ∠A_2 Ω W_1 | = | A_2. Distances involving the point W_i satisfy ((W_3 A_1)^_)/((W_3 A_2)^_) = (a_2 sin ω)/(a_1 sin(A_3 - ω)) = (a_2/a_3)^2, where ω is the Brocard angle.

Brocard axis | Brocard circle | Brocard diameter | Brocard points | Brocard triangles | isogonal conjugate | symmedian point | triangle median