Definition:Circumscribe/Circle around Polygon

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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

The more archaic circumscribed without can sometimes be seen, as well as circumscribed outside and circumscribed about.

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 $3$)