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de Longchamps Circle


deLongchampsCircle

The de Longchamps circle is defined as the radical circle of the power circles of a given reference triangle. It is defined only for obtuse triangles.

It is the complement of the polar circle.

It has circle function

 l=-(a^2)/(bc),

corresponding to Kimberling center X_(32). Its center is the de Longchamps point L (X_(20)), and its radius is

 R_L=4Rsqrt(-cosAcosBcosC),

where R is the circumradius of the reference triangle.

No Kimberling centers lie on the de Longchamps circle.


See also

de Longchamps Ellipse, Orthogonal Circles, Power Circles, Radical Circle

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Cite this as:

Weisstein, Eric W. "de Longchamps Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deLongchampsCircle.html

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