Outer Napoleon Circle


The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus concentric with the inner Napoleon circle) and radius


where Delta is the area of the reference triangle.

It has circle function


where S and S_A are Conway triangle notation. This function corresponds to the second isodynamic point S^', which is Kimberling center X_(16).

The only Kimberling center lying on it is X_(14), the second Fermat point.

The following table gives pairs of inverse Kimberling centers with respect to the outer Napoleon circle.

centernameinverse centername
X_(13)first Fermat pointX_(16)second isodynamic point
X_(383)Euler line intercept of line X_(14)X_(98)X_(1316)fifth Moses intersection
X_(616)anticomplement of X_(13)X_(624)complement of X_(16)
X_(617)anticomplement of X_(14)X_(619)complement of X_(14)
X_(618)complement of X_(13)X_(622)anticomplement of X_(16)

See also

Inner Napoleon Circle, Outer Napoleon Triangle

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Cite this as:

Weisstein, Eric W. "Outer Napoleon Circle." From MathWorld--A Wolfram Web Resource.

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