The Lucas tangents triangle (a term coined here for the first time) is the triangle Δ T_A T_B T_C formed by the pairwise tangents of the Lucas circles of a given reference triangle Δ A B C. It has trilinear vertex matrix [a b c cos A | b(2Δ + a c cos B) | c(2Δ + a b cos C) a(2Δ + b c cos A) | a b c cos B | c(2Δ + a b cos C) a(2Δ + b c cos A) | b(2Δ + a c cos B) | a b c cos C], where Δ is the area of the reference triangle. The following table gives the centers of the Lucas tangents triangle in terms of the centers of the reference triangle for Kimberling centers X_n with n<=100.

Lucas central circle | Lucas circles | Lucas circles radical circle