The Gallatly circle is the circle with center at the Brocard midpoint and radius
(1)
 
(2)

where is the circumradius of the reference triangle and is the Brocard angle.
It has circle function
(3)

corresponding to Kimberling center .
It is a Tucker circle with parameter
(4)

and parametric angle
(5)

where is the Brocard angle.
The Gallatly circle passes through Kimberling centers and (the intersections with the Brocard axis).