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.
If a rectilinear figure is circumscribed about a circle, then the circle is said to be inscribed in that figure.
The pentagon is circumscribed about a circle and the circle is inscribed in the pentagon:
Proofs: 2 3 4
Propositions: 5 6 7 8