The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle. The chord function is defined geometrically as shown in the picture. The circle was of diameter 120, and the chord lengths are accurate to two base-60 digits after the integer part.
In the second century AD, Ptolemy of Alexandria compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from 1 / 2 to 180 degrees by increments of 1 / 2 degree. The first known trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7 + 1 / 2 degrees. In trigonometry Ĭhords were used extensively in the early development of trigonometry. The midpoints of a set of parallel chords of a conic are collinear ( midpoint theorem for conics). If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP.A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle.Equal chords are subtended by equal angles from the center of the circle.Chords are equidistant from the center if and only if their lengths are equal.Among properties of chords of a circle are the following:
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