Definition:Incircle

Definition

Let $P$ be a polygon.

Let $C$ be a circle which is inscribed within $P$.

Then $C$ is an incircle of $P$.

Incenter

The center of an incircle of a polygon is called an incenter of the polygon.

Inradius

A radius of an incircle of a polygon is called an inradius of the polygon.

In the above diagram, $OG$ is an inradius of the polygon $ABCDEF$.

Also see

• Definition:Incircle of Triangle

• Results about incircles can be found here.

Sources

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