Definition:Circumscribe/Polygon around Circle

Definition

A polygon is circumscribed around a circle when each of its sides is tangent to the circumference of 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 $4$)

Also known as

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

• circumscribed outside
• circumscribed about
• circumscribed by

The more archaic circumscribed without can also occasionally be encountered.

Also see

Note that such a circle can also be described as being inscribed in the 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 $5$)

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