Inscribed

Inscribed is an adjective used in geometry and related areas to describe a relation in which a figure is placed inside another figure with certain boundary points lying on the boundary of the outer figure. The most common case is a polygon drawn inside a circle, such that all vertices lie on the circle. The enclosing circle is called the circumcircle of the polygon, and the polygon is said to be cyclic.

An inscribed circle, or incircle, is a circle tangent to all sides of a polygon. The polygon is said to be tangential. In triangles, the incircle always exists and its center is the incenter, where the angle bisectors meet. Larger polygons may or may not admit an incircle.

An inscribed angle is an angle formed by two chords of a circle that share a vertex on the circle. The measure of an inscribed angle equals half the measure of the intercepted arc. A cyclic quadrilateral—the polygon inscribed in a circle—has the property that opposite angles sum to 180 degrees, and several other relations apply.

In ordinary English, inscribed also means written, carved, or engraved on a surface, as in inscriptions on monuments or rings.