# Basic Parameters of the Kimberling Center X(46)

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 perspector of the excentral triangle (shown in purple) and the orthic triangle (shown in orange) [1].

[more]

Let

, , be the side lengths,

, , be the exradii of the excircles opposite , , ,

, , 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

## 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

[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Nov 28, 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