# Definition:Inscribe/Circle in Polygon

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## Definition

A circle is **inscribed in** a polygon when it is tangent to each of the sides of that polygon:

In the words of Euclid:

*Similarly a circle is said to be***inscribed in a figure**when the circumference of the circle touches each side of the figure in which it is inscribed.

(*The Elements*: Book $\text{IV}$: Definition $5$)

## Also known as

The more archaic language **inscribed within** is often seen.

## Also see

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

In the words of Euclid:

*A rectilineal figure is said to be***circumscribed about a circle**, when each side of the circumscribed figure touches the circumference of the circle.

(*The Elements*: Book $\text{IV}$: Definition $4$)