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Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
As an example, the area is one quarter the circle when θ ~ 2.31 radians (132.3°) corresponding to a height of ~59.6% and a chord length of ~183% of the radius. [ clarification needed ] Etc.
A chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle whose diameter is 120 parts. Ptolemy used a circle whose diameter is 120 parts. He tabulated the length of a chord whose endpoints are separated by an arc of n degrees, for n ranging from 1 / 2 to 180 by increments of 1 / 2 .
The central angle between the two points can be determined from the chord length. The great circle distance is proportional to the central angle. The great circle chord length, , may be calculated as follows for the corresponding unit sphere, by means of Cartesian subtraction:
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.
Consider the chord with the same endpoints as the arc. Its perpendicular bisector is another chord, which is a diameter of the circle. The length of the first chord is W, and it is divided by the bisector into two equal halves, each with length W / 2 . The total length of the diameter is 2r, and it is divided into two parts by the first ...
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.
The length of the arc is one third of the circumference of the circle, therefore the probability that a random chord is longer than a side of the inscribed triangle is 1 / 3 . Random chords, selection method 2 The "random radial point" method: Choose a radius of the circle, choose a point on the radius and construct the chord through ...