Basic Parameters of the Bevan Point (X40)

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Given a triangle , the Bevan point is the circumcenter of the excentral triangle (shown in orange) of [1].

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is on the incenter-circumcenter line and the orthocenter-mittenpunkt line .

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.

Then

,

,

.

You can drag the vertices , and .

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

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.

Permanent Citation

Minh Trinh Xuan

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