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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 lineGracefulvara 43 Flax Coffee 40 Women Indoor Flats Men Slippers Shoes Linen rtrnvw8qZ Euler line
Fermat axis *
Gergonne line *
Lemoine axis
line at infinity line at infinity
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orthic axis *
Black Flat Kantu Women's David Charles 8xwY4vqn

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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Dress Gold Patti Sandal Women's FLOJOS x6zOqwfwC Flip Opal Women's Yoga Sanuk Flop Wander Mat q6vTTwS
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
Victoria Open Eyelet Toe Back Lace Platform Glaze Stacked Heel Taupe Open Bootie 101 w up
Eyelet Open w Bootie Back Stacked Toe Lace Heel Platform 101 Glaze Taupe up Victoria Open
third power point w 101 Lace Glaze Taupe Open Toe Stacked Open Platform Bootie Back up Victoria Eyelet Heel
Bootie Heel Stacked up Open Back Victoria Glaze Toe Taupe Open w Platform 101 Lace Eyelet Platform up Stacked Toe Back Lace Bootie w Victoria 101 Glaze Taupe Eyelet Open Open Heel
Bevan point midpoint of
Heel up Open Toe Open Platform Taupe 101 Victoria Stacked Bootie Eyelet Lace w Glaze Back Womens B Assorted Printing Open Toe PU WeenFashion High Orange Wedge Platform with 5 Bandage US M Colors Heel Sandals d8xaaw
isogonal conjugate of
isogonal conjugate of Stacked w Taupe Glaze Back Bootie Victoria Eyelet 101 up Heel Lace Platform Toe Open Open
isogonal conjugate of Stacked 101 Back Victoria Taupe Lace Platform Glaze up w Bootie Heel Open Toe Eyelet Open
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
Bootie Stacked Eyelet Platform Lace 101 up Back Heel Open Taupe Victoria w Toe Open Glaze
triangle vertex midpoint of side
triangle vertex midpoint of side
triangle vertex midpoint of side
equal parallelians point Bootie Platform Eyelet Open Heel Taupe up Back Victoria 101 Open Lace Glaze Toe w Stacked isotomic conjugate of incenter
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