Circleenclosed

Circleenclosed is a nonstandard term used in geometry and computer science to describe the relationship in which a circle lies entirely inside another geometric object or region. In formal terms, a circle is circle-enclosed by a region if the circle is a subset of that region (all points on and inside the circle are contained within the region’s boundary). The concept emphasizes containment rather than tangency, though in many cases the circle may touch the boundary at one or more points.

In contrast to circleenclosed, standard terminology distinguishes several related ideas. An inscribed circle (incircle) is a circle contained within a polygon and tangent to its sides. A circumscribed circle (circumcircle) passes through all vertices of a polygon, enclosing the shape. The smallest circle that encloses a given set of points or region is the minimum enclosing circle (MEC), also known as the smallest enclosing circle or bounding circle. These terms highlight different containment directions: inscribed versus enclosing versus circumscribed.

Computationally, determining whether a circle is enclosed by a region or finding the largest circle that can fit inside a region are common problems in computational geometry. For polygons, the maximum enclosed circle relates to the distance from a chosen center to the boundary; for point sets, MEC algorithms identify a circle that contains all points with minimum radius. Applications include computer graphics, robotics, geographic information systems, and packing optimizations.

In practice, circleenclosed may appear as a descriptive label or a function name in software to test containment, but it is not a standard mathematical term. See also incircle, circumcircle, and minimum enclosing circle.