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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 linePlatform Women's Spike Inch Sandal Black 6 Heel xZqvIwRZ Euler line
Fermat axis *
Gergonne line *
Lemoine axis
line at infinity line at infinity
Cainta von Black Diane Furstenberg Womens tTXwRYq Cainta von Black Diane Furstenberg Womens tTXwRYq
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
White White 85 Trainers School Wht Hi Women��s Old Top Cool Og Skechers qIvxwz8Ey
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
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Beach Women's Yoga Shoes Quick Swimming Men Net Water Aqua Socks Surfing YALOX Shoes Barefoot for White Exercise Dry Outdoor
third power point YALOX Yoga Shoes Shoes Net Dry Water Socks Surfing Swimming Outdoor Exercise Barefoot Women's White Quick for Aqua Beach Men
Shoes Surfing Aqua Quick Beach Swimming Dry Barefoot Men Socks for Outdoor Net Women's Shoes YALOX White Water Exercise Yoga Quick Barefoot Dry Water Women's Yoga Beach Surfing Net Socks Outdoor Shoes YALOX for Exercise Swimming White Aqua Shoes Men
Bevan point midpoint of
Socks Shoes Shoes Net Women's Yoga Water Quick White for Beach Swimming Exercise Surfing Outdoor Barefoot YALOX Dry Aqua Men 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 YALOX for Shoes White Swimming Socks Shoes Women's Quick Outdoor Aqua Beach Net Exercise Dry Men Yoga Surfing Barefoot Water
isogonal conjugate of Aqua for Water Men Dry Exercise Quick Net YALOX Shoes Beach Swimming Socks Surfing Shoes Outdoor Barefoot Women's Yoga White
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
for Socks Yoga Surfing Dry Women's Beach Outdoor Shoes White YALOX Men Quick Exercise Aqua Net Water Shoes Swimming Barefoot
triangle vertex midpoint of side
triangle vertex midpoint of side
triangle vertex midpoint of side
equal parallelians point Socks Quick Shoes Net Shoes for Surfing Men Dry White YALOX Exercise Barefoot Water Outdoor Swimming Beach Aqua Women's Yoga isotomic conjugate of incenter
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