The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function
 |
(1)
|
corresponding to Kimberling center 
, and its radius is
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is the area of the reference
triangle, 
is the circumradius of the
reference triangle, and 
is the Brocard angle
(P. Moses, pers. comm., Jan. 3, 2005).
Its circle function is
 |
(4)
|
corresponding the triangle centroid 
and Kimberling center 
.
No Kimberling centers lie on the circle.
It is orthogonal to the Parry circle.
