Trilinear Pole

Given a line having trilinear coordinate equation


with respect to a reference triangle DeltaABC, the point


is called the trilinear pole of the line with respect to DeltaABC (Kimberling 1998, p. 38).

The following table gives the trilinear poles for some named lines.

Let A^' be the intercept of the line l and BC, and let A^('') be the harmonic conjugate of A^' with respect to B and C. Similarly define B^('') and C^(''). Then A^('')B^('')C^('') is the Cevian triangle of the trilinear pole of l.

See also

Pole, Trilinear Polar

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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 Pole

Cite this as:

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

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