Basic Parameters of the Kimberling Center X(42)

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Given a triangle , the Kimberling center is the crosspoint of the incenter and the symmedian point [1]. lies on the incenter-centroid line .

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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 , , .

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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 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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