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Concept# Chord (geometry)

Summary

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse. A chord that passes through a circle's center point is the circle's diameter.
The word chord is from the Latin chorda meaning bowstring.
In circles
Circle#Chord
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.

# 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 conics
The midpoints o

Official source

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