# Basic Parameters of the Kimberling Center X(66)

Initializing live version

Requires a Wolfram Notebook System

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

The Exeter point of triangle is the perspector of the tangential triangle and the circumcevian triangle of the centroid of (see Related Links).

[more]

The Kimberling center is the isogonal conjugate of [1].

Let

, , be the side lengths,

, , be the circumradius, inradius and semiperimeter of ,

, , be the exact trilinear coordinates of with respect to and .

Introduce the parameters , , and in Conway notation, where is the Brocard angle.

Then

,

,

.

You can drag the vertices , and .

[less]

Contributed by: Minh Trinh Xuan (October 12)
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." (Aug 2, 2023) 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