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 (and is thus concentric with the outer Napoleon circle) and radius

(1)

where is the area of the reference triangle.

It has circle function

			(2)
			(3)

where and are Conway triangle notation. This function corresponds to the first isodynamic point , which is Kimberling center .

The only Kimberling center lying on it is , the first Fermat point.

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

center	name	inverse center	name
	second Fermat point		first isodynamic point
	anticomplement of		complement of
	anticomplement of		complement of
	complement of		anticomplement of
	intercept of Euler line and line		fifth Moses intersection