 # Basic Parameters of the Kimberling Center X(43)

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Given a triangle , the center is the intersection of the lines (incenter-centroid) and (Bevan point-center of the Apollonius circle) .

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Let , , be the side lengths, , , be the circumradius, inradius and semiperimeter of , , , be the exact trilinear coordinates of with respect to and .

Then , , .

You can drag the vertices , and .

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Contributed by: Minh Trinh Xuan (August 25)
Open content licensed under CC BY-NC-SA

## 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

 C. Kimberling. "Encyclopedia of Triangle Centers." (Nov 17, 2022) faculty.evansville.edu/ck6/encyclopedia.

## Snapshots   ## Permanent Citation

Minh Trinh Xuan

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