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Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
In mathematics, a chord diagram consists of a cyclic order on a set of objects, together with a one-to-one pairing (perfect matching) of those objects. Chord diagrams are conventionally visualized by arranging the objects in their order around a circle , and drawing the pairs of the matching as chords of the circle.
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
In mathematical analysis, the universal chord theorem states that if a function f is continuous on [a,b] and satisfies () = ...
Any straight line segment connecting two points on a circle or ellipse is called a chord. Any chord in a circle which has no longer chord is called a diameter, and any segment connecting the circle's center (the midpoint of a diameter) to a point on the circle is called a radius.
A chord is the line segment that joins two distinct points of a circle. A chord is therefore contained in a unique secant line and each secant line determines a unique chord. In rigorous modern treatments of plane geometry, results that seem obvious and were assumed (without statement) by Euclid in his treatment, are usually proved.
The term chord function may refer to: Diatonic function – in music, the role of a chord in relation to a diatonic key; In mathematics, the length of a chord of a circle as a trigonometric function of the length of the corresponding arc; see in particular Ptolemy's table of chords .
When the arc reaches 60°, the chord length is exactly equal to the number of degrees in the arc, i.e. chord 60° = 60. For arcs of more than 60°, the chord is less than the arc, until an arc of 180° is reached, when the chord is only 120. The fractional parts of chord lengths were expressed in sexagesimal (base 60) numerals. For example ...