The Lucas tangents triangle (a term coined here for the first time) is the triangle formed by the pairwise tangents of the Lucas circles of a given reference triangle .

It has trilinear vertex matrix

where 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 with .

center of Lucas tangents triangle | center of reference triangle | ||

circumcenter | isogonal conjugate of | ||

first isodynamic point | first isodynamic point | ||

second isodynamic point | second isodynamic point |

The following table summarizes some perspectors of the Lucas tangents triangle and other named triangles.

triangle | Kimberling | perspector |

Lucas inner triangle | ||

symmedial triangle |