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.

Brocard circle | circle-circle intersection | D-triangle | first Brocard triangle | McCay circles | nine-point center | second Brocard triangle | Steiner points | Tarry point | third Brocard triangle