The Gallatly circle is the circle with center at the Brocard midpoint and radius
(1)
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(2)
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where is the circumradius of the reference triangle and is the Brocard angle.
It has circle function
(3)
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corresponding to Kimberling center .
It is a Tucker circle with parameter
(4)
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and parametric angle
(5)
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where is the Brocard angle.
The Gallatly circle passes through Kimberling centers and (the intersections with the Brocard axis).