Definition:Inscribe/Polygon in Circle

Definition

A polygon is inscribed in a circle when each of its vertices lies on the circumference of the circle:

In the words of Euclid:

A rectilineal figure is said to be inscribed in a circle when each angle of the inscribed figure lies on the circumference of the circle.

(The Elements: Book $\text{IV}$: Definition $3$)

Also known as

The more archaic language inscribed within is often seen.

Also see

Note that such a circle can also be described as being circumscribed around the polygon.

In the words of Euclid:

A circle is said to be circumscribed about a figure when the circumference of the circle passes through each angle of the figure about which it is circumscribed.

(The Elements: Book $\text{IV}$: Definition $6$)