# Definition:Inscribe/Polygon in Polygon

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## Definition

A polygon is **inscribed in** another polygon when each of its vertices lies on the corresponding side of the other polygon.

In the words of Euclid:

*A rectilineal figure is said to be***inscribed in a rectilineal figure**when the respective angles of the inscribed figure lie on the respective sides of that in which it is inscribed.

(*The Elements*: Book $\text{IV}$: Definition $1$)

## Also known as

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

## Also see

The second polygon also can be described as being circumscribed around the first polygon.

In the words of Euclid:

*Similarly a figure is said to be***circumscribed about a figure**when the respective sides of the circumscribed figure pass through the respective angles of that about which it is circumscribed.