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Definition: 4.6: Circumscribing Circles about Rectilinear Figures

And a circle is said to be circumscribed about a rectilinear (figure) when the circumference of the circle touches each angle of the (rectilinear) figure about which it is circumscribed.

Modern Formulation

If a rectilinear figure is inscribed in the circle, then the circle is said to be circumscribed about the figure.

Example

The pentagon is inscribed in a circle and the circle is circumscribed about the pentagon:

Mentioned in:

Corollaries: 1
Proofs: 2 3 4 5 6 7 8 9 10
Propositions: 11 12 13

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References

Adapted from (subject to copyright, with kind permission)

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