The Lucas central triangle (a term coined here for the first time) is the triangle Δ L_A L_B L_C formed by the centers of the Lucas circles of a given reference triangle Δ A B C. It has trilinear vertex matrix [a(2S + S_A) | b S_B | c S_C a S_A | b(2S + S_B) | c S_C a S_A | b S_B | c(2S + S_C)], where S, S_A, S_B, and S_C is Conway triangle notation.

Lucas central circle | Lucas circles | Lucas circles radical circle | Lucas tangents triangle

Édouard Lucas