A central circle is a circle with trilinear equation
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such that 
is a triangle center and 
is a homogeneous function that is symmetric in the side lengths
, 
, and 
of the reference triangle.
In this work, the term "circle function" is used to refer to the function 
corresponding to 
. A triangle center 
that is equal to 
modulo factors symmetric in 
, 
, 
and 
, 
, and 
is then said to correspond to the circle function 
. Circles with centers 
corresponding to a given circle function 
therefore have the same radical
line with the circumcircle with 
.
The circle function of a circle is related to the 
-power (i.e., the circle power
with respect to the 
-vertex)
by
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