The first Brocard point Ω is the interior point Ω (also denoted τ_1 or Z_1) of a triangle Δ A B C with points labeled in counterclockwise order for which the angles ∠Ω A B, ∠Ω B C, and ∠Ω C A are equal, with the unique such angle denoted ω and called the Brocard angle. The first Brocard point Ω fails to be a triangle center because it is bicentric with the second Brocard point Ω', but it has trilinear coordinates c/b :a/c :b/a (Kimberling 1998, p. 47).

Brocard angle | Brocard midpoint | Brocard points | second Brocard point | third Brocard point