The Leonine triangle Δ X_A X_B X_C (a term coined here for the first time), is the Cevian triangle of Kimberling center X_598. It is the polar triangle of the Lemoine inellipse. It has the trilinear vertex matrix [0 | (a c)/(-2 a^2 + b^2 - 2c^2) | (a b)/(-2 a^2 - 2b^2 + c^2) (b c)/(a^2 - 2b^2 - 2c^2) | 0 | (a b)/(-2 a^2 - 2b^2 + c^2) (b c)/(a^2 - 2b^2 - 2c^2) | (a c)/(-2 a^2 + b^2 - 2c^2) | 0]. The vertices are the points of contact of the Lemoine inellipse with the sidelines of the reference triangle.
Emile Michel Hyacinthe Lemoine
