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# Longuet-Higgins Circle

The Longuet-Higgins circle is the radical circle of the circles centered at the vertices , , and of a reference triangle with respective radii , , and . Its center is called the Longuet-Higgins point and is Kimberling center . It has radius

where is the circumradius of the reference triangle, and circle function

which corresponds to Kimberling center .

Longuet-Higgins Point, Moses-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.

## Referenced on Wolfram|Alpha

Longuet-Higgins Circle

## Cite this as:

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