Basic Parameters of the de Longchamps Point

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Let and
be the orthocenter and circumcenter of a triangle
. The de Longchamps point
is the reflection of
in
[1]. The point
is also the orthocenter of the anticomplementary triangle (shown in purple) of
.
Contributed by: Minh Trinh Xuan (January 2023)
Open content licensed under CC BY-NC-SA
Snapshots
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.
Reference
[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Sep 7, 2022) faculty.evansville.edu/ck6/encyclopedia.
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