A circular sector is shaded in green

A circular sector or circle sector, also known as a pie piece, is the portion of a circle enclosed by two radii and an arc. Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the Remote Authentication Dial In User Service ( RADIUS) is a networking protocol that provides centralized access authorization and accounting management for people or computers In Geometry, an arc is a closed segment of a Differentiable Curve in the two-dimensional plane; for example a circular Its area can be calculated as described below.

Let θ be the central angle, in radians, and r the radius. central angle is an Angle whose Line is the center of a Circle, and whose sides pass through a pair of points on the circle thereby Subtending The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 The total area of a circle is πr². The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and 2π (because the area of the sector is proportional to the angle, and 2π is the angle for the whole circle):

Also, if θ refers to the central angle in degrees, a similar formula can be derived. This article describes the unit of angle For other meanings see Degree.

Sectors can have special relationships, which include halves, quadrants, and octants. An octant is one of eight divisions Octant in the plane An octant is one of 8 parts of the two-dimensional Euclidean coordinate system

The length, L, of the perimeter of a sector is given by the following formula:

where θ is in degrees.

See also

• Circular segment - the part of the sector which remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary. In Geometry, a circular segment (also circle segment) is an area of a Circle informally defined as an area which is "cut off" from the rest of
• conic section

External links

• Definition and properties of a circle sector With interactive animation
• Wolfram MathWorld: Circular Sector