Chord

Pronunciation: /kɔrd/ Explain

Click on the blue points and drag them to change the figure. Click on the check boxes to see different attributes of a chord.

Describe the chord with an apothem that is zero length. Describe the chord with a sagitta that is zero length.
Manipulative 1 - Chord Created with GeoGebra.

A chord is a line segment joining two distinct points on a curve, usually a circle.[1][2]

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 that subtend the end points of the chord 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.

References

  1. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. 2nd edition. pg 46-47. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 8/6/2018. http://www.archive.org/stream/mathengineer00kellrich#page/46/mode/1up/search/chord`. Buy the book

Cite this article as:

McAdams, David E. Chord. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/chord.html.

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Revision History

6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/11/2010: Added "References". (McAdams, David E.)
11/25/2008: Initial version. (McAdams, David E.)

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