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 . lies on the incenter-centroid line .[more]
, , be the side lengths ,
, , be the circumradius, inradius and semiperimeter of ,
, , be the exact trilinear coordinates of with respect to and .
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 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
 C. Kimberling. "Encyclopedia of Triangle Centers."