Circumscribed and Inscribed Circle

Circumscribed Circle

If a polygon is drawn in a circle so that every corner of the polygon lies on the circle, the polygon is called an inscribed polygon and the circle is called the circumscribed circle. In the figure, $$O$$ is the center of the polygon and $$OF$$ is the radius of the circumscribed circle and is denoted by $$R$$.

 

Inscribed Circle

If a polygon is drawn outside a circle so that every side of the polygon touches the circle, the polygon is called the circumscribed polygon and the circle is called the inscribed circle. In the figure, $$OG$$ is the radius of the inscribed and is denoted by $$r$$.

If the polygon is regular then the center of the circle is also the center of the polygon.