Basic Parameters of the Kimberling Center X41

Given a triangle , is the symmedian point and is the insimilicenter. The Kimberling center is the crosspoint of and of [1].
Let
, , be the side lengths,
, , be the circumradius, inradius and semiperimeter of ,
, , be the exradii of the excircles opposite , , ,
,
, , be the exact trilinear coordinates of with respect to and .
Then
,
,
.
You can drag the vertices , and .

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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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