Definition:Inscribe/Polygon in Circle

Definition

A polygon is inscribed in a circle when each of its vertices lies on the circumference of the circle:

That is, the vertices are concyclic.

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 $3$)

Also known as

The more archaic language inscribed within is often seen.

Also see

• Definition:Circle Circumscribed around Polygon

• Results about inscribe can be found here.

Sources

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