Circle

Circle

A circle is a simple closed shape. 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.

Video: Geometry: Introduction to Circles - radius, diameter, circumference and area of a circle

A circle is a simple closed curve that 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 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.

Terminology

  • Annulus: the ring-shaped object, the region bounded by two concentric circles.
  • Arc: any connected part of the circle.
  • Centre: the point equidistant from the points on the circle.
  • Chord: a line segment whose endpoints lie on the circle.
  • Circumference: the length of one circuit along the circle, or the distance around the circle.
  • Diameter: a line segment whose endpoints lie on the circle and which passes through the centre; or the length of such a line segment, which is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord, and it is twice the radius.
  • Disc: the region of the plane bounded by a circle.
  • Lens: the intersection of two discs.
  • Passant: a coplanar straight line that does not touch the circle.
  • Radius: a line segment joining the centre of the circle to any point on the circle itself; or the length of such a segment, which is half a diameter.
  • Sector: a region bounded by two radii and an arc lying between the radii.
  • Segment: a region, not containing the centre, bounded by a chord and an arc lying between the chord's endpoints.
  • Secant: an extended chord, a coplanar straight line cutting the circle at two points.
  • Semicircle: an arc that extends from one of a diameter's endpoints to the other. In non-technical common usage it may mean the diameter, arc, and its interior, a two dimensional region, that is technically called a half-disc. A half-disc is a special case of a segment, namely the largest one.
  • Tangent: a coplanar straight line that touches the circle at a single point.

Chord, secant, tangent, radius, and diameter

Arc, sector, and segment
Analytic results

Length of circumference

Video: Circumference of a Circle

The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. Thus the length of the circumference C is related to the radius r and diameter d by:

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