Given a triangle , let be its circumcenter. Then the Kosnita triangle is defined to have its vertices at the circumcenters of the circumcircles of , and .

Given a triangle , the Kimberling center is the homothetic center of the intangents triangle (purple) and the Kosnita triangle (orange) [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 , , , in Conway notation, where is the Brocard angle.

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.