The anticomplement of a point in a reference triangle is a point satisfying the vector equation
(1)
|
where is the triangle centroid of (Kimberling 1998, p. 150).
The anticomplement of a point with center function is therefore given by the point with trilinears
(2)
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The anticomplement of a line
(3)
|
is given by the line
(4)
|
The following table summarizes the anticomplements of a number of named lines, including their Kimberling line and center designations.
The following table summarizes the anticomplements of a number of named circles.
circle | anticomplement |
circumcircle | anticomplementary circle |
de Longchamps circle | polar circle |
nine-point circle | circumcircle |
The following table lists some points and their anticomplements using Kimberling center designations.