tripolar

Given a triangle center X = l:m:n, the line m n α + n l β + l m γ = 0, where α:β:γ are trilinear coordinates, is called the trilinear polar. The isogonal conjugate X^(-1) = l^(-1) :m^(-1) :n^(-1) of X therefore has trilinear polar l α + m β + n γ = 0. The following table gives the trilinear polars of a number of triangle centers.

Chasles's polars theorem | isogonal conjugate | polar | trilinear pole