Lucas Tangents Triangle


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

It has trilinear vertex matrix

 [abccosA b(2Delta+accosB) c(2Delta+abcosC); a(2Delta+bccosA) abccosB c(2Delta+abcosC); a(2Delta+bccosA) b(2Delta+accosB) abccosC],

where Delta 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.

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

Lucas inner triangle5cosA+3sinA
symmedial triangleX_3cosA

See also

Lucas Central Circle, Lucas Circles, Lucas Circles Radical Circle

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Lucas Tangents Triangle." From MathWorld--A Wolfram Web Resource.

Subject classifications