Basic Parameters of the Kimberling Center X(50)
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In a triangle , if two points have barycentric coordinates and , then the point with barycentric coordinates is called their barycentric product.[more]
The line known as the Brocard axis passes through the circumcenter , the symmedian point and the isodynamic points and .
The center lies on the Brocard axis and is the barycentric product of and .
be the side lengths,
be the circumradius, inradius and semiperimeter,
, , be the exact trilinear coordinates of with respect to and .
Introduce the parameters , , and in Conway notation, where is the Brocard angle.
You can drag the vertices .[less]
Contributed by: Minh Trinh Xuan (January 2023)
Open content licensed under CC BY-NC-SA
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: even center
 C. Kimberling. "Encyclopedia of Triangle Centers." (Dec 13, 2022) faculty.evansville.edu/ck6/encyclopedia.