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 
.
