Lucas Tangents Triangle

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