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  |
