Pronunciation: /kɔrd/ ?

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Manipulative 1: Parts of a circle. Created with GeoGebra.

A chord is a line segment joining two distinct points on a curve, usually a circle.[1][2] Click on the blue points in manipulative 1 and drag them to change the figure. Click on the check boxes in manipulative 1 to see various properties of chords illustrated.

An apothem is a line segment extended from the bisector of the chord to the center of the circle.[2] page 110 A sagitta extends from the bisector of the chord to the edge of the circle in the same line as the apothem.

Any angle whose vertex is on the circle and whose legs pass through the end points of the chord is a subtended angle of the chord.[3]

The arc cut off by the chord is called the arc of the chord.

Properties of Chords

  • The perpendicular bisector of a chord passes through the center of the circle.
  • The apothem and sagitta of a chord together make a radius of the circle.
  • All angles subtended on the same side of a circle are equal.
  • A chord is a diameter of the circle iff it passes through the center of the circle.
  • Chords are equidistant from the center of the circle iff they are the same length.


  1. chord. WordNet. Princeton University. (Accessed: 2011-01-08).
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, 2nd edition, pg 46-47. D. Van Nostrand Company, 1908. (Accessed: 2010-01-11).`.
  3. subtend. WordNet. Princeton University. (Accessed: 2011-01-08).

Cite this article as:

Chord. 2010-01-11. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-01-11: Added "References" (McAdams, David.)
2008-11-25: Initial version (McAdams, David.)

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