A circumscribed circle is a circle that passes through all the vertices of a polygon. For a triangle, this circle is known as the circumcircle, and its center is called the circumcenter. The radius of the circumscribed circle is the distance from the circumcenter to any of the triangle's vertices. In a regular polygon, the circumscribed circle is centered at the polygon's center, and all vertices are equidistant from this center. The concept of a circumscribed circle is important in geometry, particularly in the study of triangles, polygons, and conic sections.