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:
“The lifelong process of caregiving, is the ultimate link between caregivers of all ages. You and I are not just in a phase we will outgrow. This is life—birth, death, and everything in between.... The care continuum is the cycle of life turning full circle in each of our lives. And what we learn when we spoon-feed our babies will echo in our ears as we feed our parents. The point is not to be done. The point is to be ready to do again.”
—Paula C. Lowe (20th century)