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,is the center of the polygon and  is the radius of the circumscribed circle and id denoted by .

 

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,  is the radius of the inscribed and is denoted by.
            If the polygon is regular then the center of the circle is called is also the center of the polygon.