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Proposition: 3.21: Angles in Same Segment of Circle are Equal

(Proposition 21 from Book 3 of Euclid's “Elements”)

In a circle, angles in the same segment are equal to one another.

• Let $ABCD$ be a circle, and let $BAD$ and $BED$ be angles in the same segment $BAED$.
• I say that angles $BAD$ and $BED$ are equal to one another.

Modern Formulation

The inscribed angles joining the ends of the same arc are equal.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1
Sections: 2

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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