Basic Parameters of the Feuerbach Point

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Given a triangle , Feuerbach's theorem states that the nine-point circle
is tangent to the three excircles and the incircle of
. The point of tangency of
with the incircle is called the Feuerbach 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 are normalized to a sum of 1.
Reference
[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Aug 15, 2022) faculty.evansville.edu/ck6/encyclopedia.
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