The Moses circle is defined as the circle with center at the Brocard midpoint 
that is tangent to the nine-point 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.
