A central circle is a circle with trilinear equation

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

CITE THIS AS:

Weisstein, Eric W. "Circle Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CircleFunction.html