Trilinear Polar

Given a triangle center X=l:m:n, the line


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

The isogonal conjugate X^(-1)=l^(-1):m^(-1):n^(-1) of X therefore has trilinear polar


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

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

See also

Chasles's Polars Theorem, Isogonal Conjugate, Polar, Trilinear Pole

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Coxeter, H. S. M. The Real Projective Plane, 3rd ed. Cambridge, England: Cambridge University Press, 1993.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Referenced on Wolfram|Alpha

Trilinear Polar

Cite this as:

Weisstein, Eric W. "Trilinear Polar." From MathWorld--A Wolfram Web Resource.

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