Basic Parameters of the Kimberling Center X(44)

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Given a triangle , the Kimberling center is the intersection of the lines (incenter-symmedian point) and (centroid-Kimberling center ) [1].

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The Kimberling center is the isogonal conjugate of [1].

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 (January 2023)
Open content licensed under CC BY-NC-SA


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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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