# Basic Parameters of the Bevan Point (X40)

Given a triangle , the Bevan point is the circumcenter of the excentral triangle (shown in orange) of [1].
is on the incenter-circumcenter line and the orthocenter-mittenpunkt line .
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 center" if its barycentric coordinates can be expressed as a function of three variables a, b, c that all occur with even exponents. If the center of a triangle has barycentric coordinates as a constant, it is called a "neutral center" (The centroid is the only "neutral center"). Conversely, a triangle center is said to be "odd center" 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."
faculty.evansville.edu/ck6/encyclopedia.

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