◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--3-circles / Proposition: 3.20: Inscribed Angle Theorem

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) $BAC$.

Modern Formulation

The central angle is double the inscribed angle.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3
Sections: 4

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References

Adapted from (subject to copyright, with kind permission)

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

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016