Chord (geometry)
geometric line segment whose endpoints both lie on the curve
In geometry, a chord (from Latin chorda 'catgut, string') 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. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").
More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's diameter.
In circles
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 of a set of parallel chords of a conic are collinear (midpoint theorem for conics).
This brief starts where responsible research should: with the source description of “Chord (geometry)” as geometric line segment whose endpoints both lie on the curve. Everything that follows is an evidence route, not borrowed authority.
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The subject matters to the general reference register because the source frames it as geometric line segment whose endpoints both lie on the curve. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Sep 21, 2026. The linked authority identifier is Q188191. None of the 0 selected statements returned an explicit reference.
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This entry incorporates text from “Chord (geometry)” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.