Inscribed Circle of a Regular Polygon
What is an Inscribed Circle?
The inscribed circle (also called the incircle) of a regular polygon is the largest circle that fits entirely inside the polygon, touching each side at exactly one point.
Formal Definition: The inscribed circle of a regular polygon is the circle that is tangent to every side of the polygon. Its center coincides with the center of the polygon, and its radius is called the apothem of the polygon.
Key Terminology
| Term | Definition |
|---|---|
| Apothem ($a$) | The perpendicular distance from the center of the polygon to the midpoint of any side. This equals the radius of the inscribed circle. |
| Circumradius ($R$) | The distance from the center to any vertex of the polygon (radius of the circumscribed circle). |
| Side length ($s$) | The length of one side of the regular polygon. |
| $n$ | The number of sides of the regular polygon. |