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Longuet-Higgins Point

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LonguetHigginsPoint

The Longuet-Higgins point is the radical center of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c, c+a, and a+b. It has triangle center function

alpha_(962)=(a^4+2a^3b-2ab^3-b^4+2a^3c-4a^2bc+2ab^2c+2abc^2+2b^2c^2-2ac^3-c^4)/a

and is Kimberling center X_(962).

See also

Longuet-Higgins Circle

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References

Kimberling, C. "Encyclopedia of Triangle Centers: X(962)=Longuet-Higgins Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X962.Longuet-Higgins, M. S. "On the Principal Centers of a Triangle." Elemente der Math. 56, 122-129, 2001.van Lamoen, F. "Problem 10734." Amer. Math. Monthly 107, 658-659, 2000.Woo, P. Y. "Solution of Problem 10734." Amer. Math. Monthly.

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Longuet-Higgins Point

Cite this as:

Weisstein, Eric W. "Longuet-Higgins Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Longuet-HigginsPoint.html

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