# Basic Parameters of the Kimberling Center X(43)

Given a triangle , the center is the intersection of the lines (incenter-centroid) and (Bevan point-center of the Apollonius circle) [1].
Let
, , be the side lengths,
, , be the exact trilinear coordinates of with respect to and .
Then
,
,
.
You can drag the vertices , and .

### DETAILS

A triangle center is said to be even when its barycentric coordinates can be expressed as a function of three variables , , that all occur with even exponents. If the center of a triangle has constant barycentric coordinates, it is called a neutral center (the centroid is the only neutral center). A triangle center is said to be odd if it is neither even nor neutral.
Standard barycentric coordinates of a point with respect to a reference triangle have a sum of 1.
Reference
[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Nov 17, 2022) faculty.evansville.edu/ck6/encyclopedia.

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