Proposition: 3.20: Inscribed Angle Theorem
(Proposition 20 from Book 3 of Euclid's “Elements”)
In a circle, the angle at the center is double that at the circumference, when the angles have the same circumference base.
* Let $ABC$ be a circle, and let $BEC$ be an angle at its center, and $BAC$ (one) at (its) circumference.
* And let them have the same circumference base $BC$.
* I say that angle $BEC$ is double (angle) $BAC$.
The central angle is double the inscribed angle.
Table of Contents
Proofs: 1 2 3
Thank you to the contributors under CC BY-SA 4.0!
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016