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Among properties of chords of a circle are the following: Chords are equidistant from the center if and only if their lengths are equal. 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.
The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
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. The number of different chord diagrams that may be given for a set of cyclically ordered objects is the double factorial ()!!. [1] There is a Catalan number of chord diagrams on a ...
A circle with five chords and the corresponding circle graph. In graph theory, a circle graph is the intersection graph of a chord diagram.That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle). If the angle subtended by the chord at the centre is 90 ° , then ℓ = r √2 , where ℓ is the length of the chord, and r is the radius of the circle.
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.
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Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY . Proof