Inscribed and Circumscribed Polygons

A combination of a polygon and a circle can be arranged in two possible ways and accordingly named as inscribed or circumscribed polygon.

What is an Inscribed Polygon

An inscribed polygon is a polygon that has all its vertices on a circle. It is also known as ‘polygon in a circle’, as the polygon is found inscribed in a circle and the circle is found to be circumscribed around the polygon.

All regular polygons starting from an equilateral triangle, a square, a pentagon, or a hexagon can be inscribed in a circle. For regular polygons inscribed in a circle:

1. The center of the polygon is also the center of the circumscribed circle
2. The radius of the polygon is also the radius of the circumscribed circle
3. A perpendicular line drawn from the center to the midpoint of any side of the polygon is the apothem

What is a Circumscribed Polygon

Also known as a tangential polygon, it is a polygon with vertices outside the circle, while its sides are tangent to the circle.

1. The polygon intersects the circle at the midpoint of each side
2. The center of the circle is equidistant from all sides of the polygon
3. The center of the polygon is also the center of the inscribed circle
4. The apothem of the polygon is the radius of the inscribed circle