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In general, the word "complement" refers to that subset of some set which excludes a given subset . Taking and its complement together then gives the whole of the original set. The notations and are commonly used to denote the complement of a set .
This concept is commonly used and made precise in the particular cases of a complement point, graph complement, knot complement, and complement set. The word "complementary" is also used in the same way, so combining an angle and its complementary angle gives a right angle and a complementary error function Black Men's Anthracite White TB Pure Air 34 Black White Nike Zoom Pegasus Platinum vdfqOv6w and the usual error function erf give unity when added together,
The complement point of a point with respect to a reference triangle , also called the inferior point, subordinate point, or medial image, is the point such that
(2)

where is the triangle centroid.
The complement point of a point with trilinear coordinates is therefore given by
(3)

The following table lists the complements of some named circles.
circle  complement 
circumcircle  ninepoint circle 
anticomplementary circle  circumcircle 
polar circle  de Longchamps circle 
The complement of a line
(4)

is given by the line
(5)

The following table summarizes the complements of a number of named lines.
The following table summarizes the complements of several common triangle centers.
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