The Moses circle is defined as the circle with center at the Brocard midpoint that is tangent to the ninepoint circle at the center of the Kiepert hyperbola .
It has 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 .
The Moses circle passes through Kimberling centers (center of the Kiepert hyperbola), , and and (which are its intersections with the Brocard axis).
Its internal and external centers of similitude with the incircle are and , respectively.