Definition: 4.7: Chord and Secant

A straight line is said to be inserted into a circle when its extremities are on the circumference of the circle.

Modern Formulation

A chord of a circle is a segment which intersects two points of the circle’s circumference.


If the chord is extended in both directions, then this line is called a secant.

Note: A the special case of a chord which goes through the center of the circle, is its diameter.

Corollaries: 1
Definitions: 2 3 4 5 6 7
Proofs: 8 9 10 11 12 13 14 15 16 17 18 19
Propositions: 20 21 22 23 24 25 26 27 28 29

Thank you to the contributors under CC BY-SA 4.0!



Adapted from CC BY-SA 3.0 Sources:

  1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

  1. Casey, John: "The First Six Books of the Elements of Euclid"


  1. Byrne, O.: "The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols are used Instead of Letters", London William Pickering, 1847

Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"