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).
