What is a chord in math?


Quick Answer

A chord is a straight line that connects two points on the curve of a circle. Unlike a secant, which is a line that extends infinitely in both directions, a chord is confined to inside the circle.

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Full Answer

Chords have several different properties. For example, a diameter goes through the center of a circle and is the circle's longest chord. Also, if the secant lines of two chords intersect, the lengths of the chords satisfy the power of a point theorem. Chords of equal lengths are also equidistant from the center of the circle.

A chord divides a circle into two distinct arcs. The shorter one is called the minor arc, and the longer one is called the major arc. Because both arcs share the same two points, they also share the same name. For example, "arc CD" can refer to either the minor or major arc. When no distinction is specified, it is assumed that the name refers to the minor arc.

Chords play an important role in trigonometry. Greek astronomer and geographer Hipparchus created an astrological trigonometric chord table based on 24 steps, and Greco-Egyptian astronomer and mathematician Ptolemy later developed a more complex table based on 180 degrees. Sines, which are modifications of chords, serve as the primary trigonometric function.

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