Circumscrit

Circumscrit is a term used in geometry to describe a polygon that has a circle passing through all of its vertices. This circle is called the circumscribed circle, or simply the circumcircle, and its center is known as the circumcenter. A polygon that has a circumcircle is called a cyclic polygon. Not all polygons are cyclic. For example, a general rectangle is cyclic, but a general parallelogram is not. Triangles, however, are always cyclic, with their circumcenter located at the intersection of the perpendicular bisectors of their sides.

The radius of the circumscribed circle is called the circumradius. For a triangle with sides a, b, and c, and area A, the circumradius R can be calculated using the formula R = abc / (4A). For a regular n-sided polygon with side length s, the circumradius can be found using the formula R = s / (2 sin(pi/n)). The existence of a circumcircle implies certain symmetries and relationships between the sides and angles of the polygon.

In some contexts, "circumscrit" can also refer to the act of drawing a circumscribed circle around a polygon. This process involves finding the circumcenter and then drawing a circle with that center and a radius equal to the distance from the center to any vertex. The concept of circumscription is fundamental in various geometric constructions and theorems.