# Chord

Pronunciation: /kÉ”rd/ 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.[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.

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 the chord are equal.
• A chord is a diameter of the circle if and only if it passes through the center of the circle.
• Chords are equidistant from the center of the circle if and only if they are the same length.

### References

1. McAdams, David E.. All Math Words Dictionary, chord. 2nd Classroom edition 20150108-4799968. pg 33. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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 6/25/2018. http://www.archive.org/stream/mathengineer00kellrich#page/46/mode/1up/search/chord. Buy the book

McAdams, David E. Chord. 4/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/chord.html.

### Revision History

4/13/2019: Corrected references. (McAdams, David E.)