Basic Parameters of the Schiffler Point

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Let be the incenter of triangle
. The Euler lines of the four triangles
,
,
,
intersect at one point, called the Schiffler point
[1].
Contributed by: Minh Trinh Xuan (January 2023)
Open content licensed under CC BY-NC-SA
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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." (Sep 15, 2022) faculty.evansville.edu/ck6/encyclopedia.
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