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Definition: 4.5: Inscribing Circles in Rectilinear Figures

And, similarly, a circle is said to be inscribed in a (rectilinear) figure when the circumference of the circle touches each side of the (figure) in which it is inscribed.

Modern Formulation

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

Example

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

Mentioned in:

Corollaries: 1
Proofs: 2 3 4
Propositions: 5 6 7 8

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References

Adapted from (subject to copyright, with kind permission)

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