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Trilinear Pole


Given a line having trilinear coordinate equation

 lalpha+mbeta+ngamma=0

with respect to a reference triangle DeltaABC, the point

 mn:nl:lm

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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References

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. https://mathworld.wolfram.com/TrilinearPole.html

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