Trilinear Polar

Given a triangle center , the line

where are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38).

The isogonal conjugate of therefore has trilinear polar

The following table gives the trilinear polars of a number of triangle centers.

Kimberling center	center	trilinear polar	line
	incenter	antiorthic axis
	triangle centroid	line at infinity
	orthocenter	orthic axis
	symmedian point	Lemoine axis
	Gergonne point	Gergonne line
	third Brocard point	de Longchamps line
		van Aubel line
	focus of the Kiepert parabola	Brocard axis
	Yff parabolic point	Nagel line
	Tixier point	Fermat axis
		Euler line
		Soddy line

The trilinear polar of is the perspectrix of the Cevian triangle of and the reference triangle .