The third Brocard triangle is Gibert's term for the isogonal conjugate of the first Brocard triangle. It has trilinear vertex matrix [b^2 c^2 | a b^3 | a c^3 a^3 b | a^2 c^2 | b c^3 a^3 c | b^3 c | a^2 b^2].

Brocard triangles | D-triangle | first Brocard triangle | second Brocard triangle

Pierre René Jean Baptiste Henri Brocard