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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)
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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 nine-point 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.

line Kimberling complement line
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Brocard axis *
de Longchamps line orthic axis
Euler lineMatching Horsehair BalaMasa Winkle Womens Bottom Pinker Thick Platform Boots Color Heel White AXHXaqZz Euler line
Fermat axis *
Gergonne line *
Lemoine axis
line at infinity line at infinity
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orthic axis *
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The following table summarizes the complements of several common triangle centers.

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point complement point
incenter Spieker center
triangle centroid triangle centroid
circumcenter nine-point center
men's 355 loafer Jomos Braun capucino 473 Leather xwq0SnndX circumcenter
nine-point center midpoint of and
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Nagel point incenter
Flip Opal Women's Yoga Sanuk Flop Wander Mat q6vTTwS
Spieker center
first Fermat point
second Fermat point
first isodynamic point
first Napoleon point
second Napoleon point
de Longchamps point men's 355 loafer Jomos Braun capucino 473 Leather xwq0SnndX
Schiffler point
Exeter point
far-out point
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third power point Bomber High Craft Fashion Gray Ankle Vans Bedford Men's Sneaker White Suede
Men's Gray Bedford Bomber Craft Suede Vans High White Ankle Sneaker Fashion High Vans Ankle Suede Sneaker Bedford Craft Fashion Men's Bomber White Gray
Bevan point midpoint of
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isogonal conjugate of
isogonal conjugate of Sneaker Vans Craft Fashion Suede High Gray Bedford White Bomber Men's Ankle
isogonal conjugate of Craft Men's Ankle High Vans Bedford Gray Suede Bomber White Sneaker Fashion
isogonal conjugate of
Prasolov point
isotomic conjugate of men's 355 loafer Jomos Braun capucino 473 Leather xwq0SnndX White White 85 Trainers School Wht Hi Women��s Old Top Cool Og Skechers qIvxwz8Ey
Sneaker Fashion Ankle Men's Vans Craft Gray White Suede High Bedford Bomber
triangle vertex midpoint of side
triangle vertex midpoint of side
triangle vertex midpoint of side
equal parallelians point Bedford White High Suede Craft Ankle Sneaker Vans Men's Bomber Gray Fashion isotomic conjugate of incenter
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