Let c_1, c_2, and c_3 be the circles through the vertices A_2 and A_3, A_1 and A_3, and A_1 and A_2, respectively, which intersect in the first Brocard point Ω. Similarly, define c_1^, , c_2^, , and c_3^, with respect to the second Brocard point Ω'. Let the two circles c_1 and c_1^, tangent at A_1 to A_1 A_2 and A_1 A_3, and passing respectively through A_3 and A_2, meet again at C_1, and similarly for C_2 and C_3. Then the triangle Δ C_1 C_2 C_3 is called the second Brocard triangle.

Brocard triangles | D-triangle | first Brocard triangle | third Brocard triangle