# Basic Parameters of the Kimberling Center X(51)

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The feet of the three altitudes of a triangle form the orthic triangle. The centroid of a triangle is both the average of the vertices and the intersection of its medians. For an arbitrary point in a triangle, the lines from that point to the vertices are known as the cevians. If the cevians are reflected by the angle bisectors they intersect at the isogonal conjugate. The symmedian point of a triangle is the isogonal conjugate of the centroid [1].

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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 center" if 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 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." (May 9, 2023) faculty.evansville.edu/ck6/encyclopedia.

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