The first Brocard point 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. It is not a triangle center, but has trilinear coordinates c/b :a/c :b/a (Kimberling 1998, p. 47). Note that extreme care is needed when consulting the literature, since reversing the order in which the points of the triangle are labeled results in exchanging the Brocard points.

Brocard angle | Brocard midpoint | Brocard triangles | equi-Brocard center | first Brocard point | mice problem | pursuit curve | second Brocard point | third Brocard point | Yff points