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 and its radius is called the circumradius.
A polygon which has a circumscribed circle is called a cyclic polygon (sometimes a concyclic polygon, because the vertices are concyclic). 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 a 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.
Read more about Circumscribed Circle: Triangles, Cyclic Quadrilaterals, Cyclic n-gons
Famous quotes containing the word circle:
“A man should not go where he cannot carry his whole sphere or society with him,Mnot bodily, the whole circle of his friends, but atmospherically. He should preserve in a new company the same attitude of mind and reality of relation, which his daily associates draw him to, else he is shorn of his best beams, and will be an orphan in the merriest club.”
—Ralph Waldo Emerson (1803–1882)