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 (and is thus concentric with the inner 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 second isodynamic point , which is Kimberling center .
The only Kimberling center lying on it is , the second Fermat point.
The following table gives pairs of inverse Kimberling centers with respect to the outer Napoleon circle.
center  name  inverse center  name 
first Fermat point  second isodynamic point  
Euler line intercept of line  fifth Moses intersection  
anticomplement of  complement of  
anticomplement of  complement of  
complement of  anticomplement of 