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Proposition: 3.22: Opposite Angles of Cyclic Quadrilateral

(Proposition 22 from Book 3 of Euclid's “Elements”)

For quadrilaterals within circles, the (sum of the) opposite angles is equal to two right angles.

• Let $ABCD$ be a circle, and let $ABCD$ be a quadrilateral within it.
• I say that the (sum of the) opposite angles is equal to two right angles.

Modern Formulation

In a quadrilateral built upon four secants of a given circle, the sum of the opposite angles is $180^\circ$.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 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