## ::Circle

### ::concepts

Circle::chord    Point::angle    Points::centre    Radius::right    Circles::geometry    Which::''r''

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A circle is a simple shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance 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 distance between any of the points and the centre is called the radius.

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 figure including its interior; in strict technical usage, the circle is the former and the latter is called a disk.

A circle may also be defined as a special 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.

A circle is a plane figure bounded by one line, and such that all right lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.
— Euclid. Elements Book I. <ref>OL7227282M </ref>

Circle sections
Intro  Terminology  History  Analytic results  Properties  Circle of Apollonius  Circles inscribed in or circumscribed about other figures  Circle as limiting case of other figures  Squaring the circle  See also  References  Further reading  External links

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