Definition:Circumscribe/Polygon around Circle
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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:
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