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Definition: 4.3: Inscribing Rectilinear Figures in Circles

A rectilinear figure is said to be inscribed in a circle when each angle of the inscribed (figure) touches the circumference of the circle.

Modern Formulation

A rectilinear figure (\(n\)-sided figure, \(n \ge 3\)) is said to be inscribed in a circle when each of its vertices is in the circumference of the circle.

Example

The pentagon is inscribed in a circle:

Mentioned in:

Definitions: 1
Proofs: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Propositions: 20 21 22 23 24 25 26 27 28 29

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References

Bibliography

1. Health L. Thomas (Transl.): "Euclid's Elements - all thirteen books", Green Lion Press, 2013,
2. Byrne, O.: "The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols are used Instead of Letters", London William Pickering, 1847

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