Given triangle Δ A_1 A_2 A_3, let the point of intersection of A_2 Ω and A_3 Ω' be B_1, where Ω and Ω' are the Brocard points, and similarly define B_2 and B_3. Then Δ B_1 B_2 B_3 is called the first Brocard triangle, and is inversely similar to Δ A_1 A_2 A_3. It is inscribed in the Brocard circle. The trilinear vertex matrix is [a b c | c^3 | b^3 c^3 | a b c | a^3 b^3 | a^3 | a b c].

Brocard triangles | D-triangle | second Brocard triangle | third Brocard triangle