A circle is a simple closed shape . It is the set of all points in a plane that are at a givendistance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distancebetween any of the points and the centre is called the radius . This article is about circles in Euclidean geometry , and, in particular, the Euclidean plane, except where otherwise noted.
A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figureincluding its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc.
A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.