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Neuberg Circles Radical Circle

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NeubergCirclesRadicalCircle

The radical circle of the Neuberg circles has circle function

l=(a^2b^4-b^4c^2+a^2c^4-b^2c^4)/(bc(a^2b^2+a^2c^2+b^2c^2)),
(1)

which does not correspond to any Kimberling center. The corresponding center is

alpha_(194)=(a^2b^2+a^2c^2-b^2c^2)/a,
(2)

corresponding to Kimberling center X_(194), and its radius is

R_R=(sqrt(f(a,b,c)))/(a^2b^2+a^2c^2+b^2c^2),
(3)

where

f(a,b,c)=a^6b^4+a^4b^6-2a^6b^2c^2+a^4b^4c^2-2a^2b^6c^2+a^6c^4+a^4b^2c^4+a^2b^4c^4+b^6c^4+a^4c^6-2a^2b^2c^6+b^4c^6.
(4)

It is orthogonal to the Stevanović circle, and no Kimberling centers lie on it.

See also

Neuberg Circles, Radical Circle

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Cite this as:

Weisstein, Eric W. "Neuberg Circles Radical Circle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NeubergCirclesRadicalCircle.html

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