# Definition:Inscribe/Polygon in Circle

< Definition:Inscribe(Redirected from Definition:Polygon Inscribed in Circle)

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## 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.