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Moses-Longuet-Higgins Circle


MosesLonguetHigginsCircle

The Moses-Longuet-Higgins circle is the radical circle of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c-a, c+a-b, and a+b-c (P. Moses, pers. comm., Nov. 17, 2005).

Its center has triangle center function

 alpha=(a^2(S_A-4s_a^2)+4(s_c^2S_B+s_b^2S_C))/a,
(1)

where S_A, S_B, and S_C are Conway triangle notation, s_a=s-a, s_b=s-b, and s_c=s-c. This is not a Kimberling center.

It has radius

 R_(MLH)=sqrt(9R^2+4[1-(12(a+b+c)R^2)/(abc)]r^2),
(2)

where R is the circumradius and r the inradius of the reference triangle, and circle function

 l=-((a-b-c)^2)/(bc),
(3)

which corresponds to Kimberling center X_(220).


See also

Longuet-Higgins Circle, Moses Circle

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Cite this as:

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

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