# Definition:Circumscribe/Circle around Polygon

< Definition:Circumscribe(Redirected from Definition:Polygon Circumscribed by Circle)

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## Definition

A circle is **circumscribed around** a polygon when its circumference passes through each of the vertices of that 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 $6$)

Not all polygons can be circumscribed.

Here is an example of one that cannot:

## Also known as

As well as **circumscribed around**, the following can also be seen:

The more archaic **circumscribed without** can also occasionally be encountered.

## Also see

Note that such a polygon can also be described as being inscribed in 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 $3$)

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**circumscribed** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**circumscribed**