Definition: 3.10: Circular Sector, Central Angle

And a sector of a circle is the figure contained by the straight lines surrounding an angle, and the circumference cut off by them, when the angle is constructed at the center of a circle.

Modern Formulation

A circular sector is the figure contained by two radii of a circle and the arch between them. The angle $\angle{BAC}$ is called a central angle.


Please note that each pair of different radii generates two circular sectors because there are two arcs whose endpoints are the endpoints of the radii. Which sector is meant, shall be made clear from the context.

Proofs: 1 2 3
Propositions: 4 5 6 7

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
  2. Prime.mover and others: "Pr∞fWiki",, 2016

Adapted from (subject to copyright, with kind permission)

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