# Basic Parameters of the Kimberling Center X(42)

Given a triangle , the Kimberling center is the crosspoint of the incenter and the symmedian point [1]. lies on the incenter-centroid line .
Let
, , be the side lengths ,
,
, , be the exact trilinear coordinates of with respect to and .
Then
,
,
.
You can drag the vertices , , .

### DETAILS

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

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