# Basic Parameters of the Kimberling Center X(38)

Given a triangle , the point is its incenter and is the isotomic conjugate of . Then the Kimberling center is the crosspoint of and of [1] (Randy Hutson, August 23, 2011).
lies on the line , where is the Schiffler point.
Let
, , be the side lengths,
,
, , be the exact trilinear coordinates of with respect to and .
Introduce the parameters , , , in Conway notation, where is the Brocard angle.
Then
,
,
.
You can drag the vertices , and .

### DETAILS

A triangle center is said to be even when 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 constant barycentric coordinates, it is called a neutral center (the centroid is the only neutral center). A triangle center is said to be odd 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." (Oct 26, 2022) faculty.evansville.edu/ck6/encyclopedia.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.