An inscribed polygon is a polygon whose vertices all lie on a single circle. This circle is known as the circumcircle, and its center is called the circumcenter. Inscribed polygons are significant in geometry because they help illustrate various properties related to angles, sides, and symmetry. For example, in an inscribed triangle, the angles opposite to each side are related to the arc lengths of the circumcircle. This relationship is useful in solving problems involving triangles, circles, and trigonometry. Inscribed polygons can be regular, like a regular hexagon, or irregular, depending on the arrangement of their vertices.