Circumscribed

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Etymology

Middle English circumscriven, from Latin circumscribere, from circum- + scribere to write, draw

Definitions

  • 1 a : to constrict the range or activity of definitely and clearly <his role was carefully circumscribed>
b : to define or mark off carefully <a study of plant species in a circumscribed area>
  • 2 a : to draw a line around
b : to surround by or as if by a boundary <fields circumscribed by tall trees>
  • 3 : to construct or be constructed around (a geometrical figure) so as to touch as many points as possible

Description

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter.

A polygon which has a circumscribed circle is called a cyclic polygon. All regular simple polygons, all triangles and all rectangles are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it. Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a circle, but every polygon has unique minimum bounding circle, which may be constructed by a linear time algorithm. Even if a polygon has a circumscribed circle, it may not coincide with its minimum bounding circle; for example, for an obtuse triangle, the minimum bounding circle has the longest side as diameter and does not pass through the opposite vertex.