Circle - Chord properties

Circle - Chord properties: Encyclopedia - Circle

A circle, in Euclidean geometry, is the set of all points at a fixed distance, called the radius, from a fixed point, the centre. The points can only be those that are part of a conic section; within the set of a plane bisecting a cone. Circles are simple closed curves, dividing the plane into an interior and exterior. Sometimes the word circle is used to mean the interior, with the circle itself called the circumference(C). Usually however, the circumference means the length of the circle, and the interior ...

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Circle - Chord properties: Encyclopedia II - Circle - Properties Circle - Chord properties. Chords equidistant from the centre of a circle are equal. Equal chords are equidistant from the centre. A line from the centre, perpendicular to a chord, bisects the chord. The line segment drawn from the centre to the midpoint of the chord is perpendicular to the chord. The perpendicular bisector of a chord passes t ...

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Circle - Chord properties: Encyclopedia - Trigonometric function

In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to comp ...

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Trigonometric function - Relationship to exponential function

Trigonometric function - Definitions via differential equations

Trigonometric function - The significance of radians

Circle - Chord properties: Encyclopedia - Pentatonic scale

In music, a pentatonic scale is a scale with five notes per octave. Pentatonic scales are very common and are found all over the world, including but not limited to the tuning of the Ethiopian krar and the Indonesian gamelan, the melodies of African-American spirituals, Celtic folk music and the music of French composer Claude Debussy. Pentatonic scale - Types of pentatonic scales. One of the most common pentatonic scales, sometimes called a major pentatonic scale or primary pentatonic scale ( ...

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Circle - Chord properties: Encyclopedia - 9 number

0 1 2 3 4 5 6 7 8 9 >> List of numbers -- Integers 0 10 20 30 40 50 60 70 80 90 >> nona- (from Latin) 9 (nine) is the natural number following 8 and preceding 10. 9 number - In mathematics. Nine is a composite number, its proper divisors being 1 and 3. It is 3 times 3 and hence the third square number. 9 is a Motzkin number. In base 10 a number is evenly divisible by nine if and only if the iterative sum of ...

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9 number - In mathematics

9 number - In numeral systems

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Circle - Chord properties: Encyclopedia - Symmetry

Symmetry is a characteristic of geometrical shapes, equations, and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by one of the operations. In 2D geometry the main kinds of symmetry of interest are with respect to the basic Euclidean plane isometries: translations, rotations, reflections, ...

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Symmetry - Mathematical model for symmetry

Symmetry - Non-isometric symmetry

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Circle - Chord properties: Encyclopedia - 3 number

0 1 2 3 4 5 6 7 8 9 >> List of numbers -- Integers 0 10 20 30 40 50 60 70 80 90 >> tre-/ter- (from Latin) 3 (three) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4. 3 number - In mathematics. Three is the first odd prime number, and the second smallest prime after two. Three is the first Fermat prime (22º + 1). Three is the first Me ...

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Circle - Chord properties: Encyclopedia - Music

Music is an art, entertainment, or other human activity which involves organized and audible sound, though definitions vary. Music - What is music?. Main article: Definitions of music Broadly, here are some groups of definitions: Those that define music as an external, physical fact, for example "organized sound", or as a specific type of perception Those that label it, according to context, as a social construction or subjective experience Those tha ...

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Circle - Chord properties: Encyclopedia - Baroque music

Baroque music describes an era and a set of styles of European classical music which were in widespread use between approximately 1600 to 1750 (see Dates of classical music eras for a discussion of the problems inherent in defining the beginning and end points). This era is said to begin in music after the Renaissance and to be followed by the Classical music era. Baroque music forms a major portion of the classical music canon, it is widely performed and studied and listened to. It is associated with composers such as J.S. Bach, Geor ...

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Baroque music - Overview

Baroque music - Brief History of Baroque Music

Circle - Chord properties: Encyclopedia - List of Star Wars races

This is a list of sentient races from the fictional universe of Star Wars. List of Star Wars races - A. List of Star Wars races - Abyssin. The Abyssin inhabit the planet Byss. They are a nomadic race, often described as "primitive and violent". They stand approximately 2 meters tall and have a humanoid appearance, with long limbs. They also possess a single large eye which dominates their greenish-tan foreheads. All Abyssins have the ability to heal ...

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List of Star Wars races - A

List of Star Wars races - B

List of Star Wars races - C

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List of Star Wars races - X

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List of Star Wars races - Z

Circle - Chord properties: Encyclopedia II - Inscribed angle - Proof

To understand this proof, it is useful to draw a diagram. Inscribed angle - 1. Inscribed angles where one chord is a diameter. Let O be the center of a circle. Choose two points on the circle, and call them V and A. Draw line VO and extended past O so that it intersects the circle at point B which is diametrically opposite the point V. Draw an angle whose vertex is point V and whose sides p ...

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