 # Basic Parameters of the Kimberling Center X(44)

Initializing live version Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Given a triangle , the Kimberling center is the intersection of the lines (incenter-symmedian point) and (centroid-Kimberling center ) .

[more]

The Kimberling center is the isogonal conjugate of .

Let , , be the side lengths, , , be the circumradius, inradius and semiperimeter of , , , be the exact trilinear coordinates of with respect to and .

Then , , .

You can drag the vertices , and .

[less]

Contributed by: Minh Trinh Xuan (January 2023)
Open content licensed under CC BY-NC-SA

## Snapshots   ## 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.

Reference

 C. Kimberling. "Encyclopedia of Triangle Centers." (Nov 17, 2022) faculty.evansville.edu/ck6/encyclopedia.

## Permanent Citation

Minh Trinh Xuan

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send