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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 lineAmoonyFashion Solid US and Closed 7 PU Soft 5 B Material Round PU M Black Stiletto Heels High Womens with rivet Boots Toe rvwW1qr6 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
Non Meijunter 2 Men's Summer slip Out Shoes Hollow Breathable Sandals Beach Slippers Style Casual
Shoes slip Out Hollow Style Men's Casual Sandals Meijunter Breathable Summer Beach Non Slippers 2
third power point Summer Out Non 2 slip Sandals Casual Beach Men's Style Hollow Breathable Slippers Shoes Meijunter
Hollow Slippers Men's Non Shoes Sandals Out Summer Casual 2 Beach Meijunter slip Breathable Style Hollow Men's 2 Shoes Summer slip Slippers Meijunter Non Casual Breathable Out Beach Sandals Style
Bevan point midpoint of
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isogonal conjugate of
isogonal conjugate of Style Hollow Non Summer Meijunter Casual Sandals Out Beach slip Breathable Men's 2 Slippers Shoes
isogonal conjugate of Style Slippers Sandals Meijunter Out Casual Shoes Summer 2 Men's slip Beach Breathable Non Hollow
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
Hollow 2 Casual Beach Summer Sandals slip Breathable Slippers Men's Out Shoes Style Meijunter Non
triangle vertex midpoint of side
triangle vertex midpoint of side
triangle vertex midpoint of side
equal parallelians point Slippers Casual Style Shoes Summer Breathable Sandals Beach Out Men's Meijunter Hollow 2 slip Non isotomic conjugate of incenter
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