Chord (geometry)
A chord of a circle is a straight line segment with both endpoints on the circle. If you extend a chord in both directions, you get a secant line. The line through the chord’s midpoint that is perpendicular to the chord is called the sagitta, or the arc’s height.
A chord can also join two points on any curve, such as an ellipse. If a chord passes through the circle’s center, it is a diameter.
Chords have interesting properties. For conic sections, the midpoints of parallel chords lie on a straight line. Chords were central to the early development of trigonometry. Hipparchus made an early chord table, and Ptolemy later expanded it, using a circle of diameter 120 for accuracy.
On a unit circle, the chord corresponding to a central angle θ (0 < θ ≤ π) is the distance between the points (1,0) and (cos θ, sin θ). This distance is sqrt(2 − 2 cos θ), which equals 2 sin(θ/2). Thus the chord function is closely related to the sine function. Ancient trig was built around chords, and a long, now-lost work by Hipparchus suggests how much was known about them. The chord function also has an inverse and follows identities similar to modern trigonometric rules.
This page was last edited on 2 February 2026, at 18:30 (CET).