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Excircles Radical Circle

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ExcirclesRadicalCircle

The radical circle of the excircles has center at the Spieker center X_(10) and radius

R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)).

Its circle function is

l=(a^3-ab^2+2abc-ac^2)/(4abc),

corresponding to X_(56), the external similitude center of the incircle and circumcircle. No Kimberling centers lie on it.

See also

Central Circle, Excircles, Radical Circle

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Cite this as:

Weisstein, Eric W. "Excircles Radical Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExcirclesRadicalCircle.html

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