Inner Napoleon Circle


The inner Napoleon circle, a term coined here for the first time, is the circumcircle of the inner Napoleon triangle. It has center at the triangle centroid G (and is thus concentric with the outer 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 first isodynamic point S, which is Kimberling center X_(15).

The only Kimberling center lying on it is X_(13), the first Fermat point.

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

centernameinverse centername
X_(14)second Fermat pointX_(15)first isodynamic point
X_(616)anticomplement of X_(13)X_(618)complement of X_(13)
X_(617)anticomplement of X_(14)X_(623)complement of X_(15)
X_(619)complement of X_(14)X_(621)anticomplement of X_(15)
X_(1080)intercept of Euler line and line X_(13)X_(98)X_(1316)fifth Moses intersection

See also

Inner Napoleon Triangle, Outer Napoleon Circle

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Cite this as:

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

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