Circular segment

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In geometry, a circular segment (symbol: ) is a region of a circle which is "cut off" from the rest of the circle by a secant or a chord. More formally, a circular segment is a region of two-dimensional space that is bounded by an arc (of less than 180°) of a circle and by the chord connecting the endpoints of the arc.

Formula[edit]

A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area).

Let R be the radius of the circle, θ is the central angle in radians, α is the central angle in degrees, c the chord length, s the arc length, h the sagitta (height) of the segment, and d the height of the triangular portion.

  • The radius is 
  • The arc length is 
  • The chord length is 
  • The sagitta is 
  • The angle is 

Area[edit]

The area of the circular segment is equal to the area of the circular sector minus the area of the triangular portion—that is,

with the central angle in radians, or

with the central angle in degrees.

See also[edit]

References[edit]

External links[edit]