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User:Eirik1231/Circular segment

From Wikipedia, the free encyclopedia

In geometry, a circular segment (symbol: ) is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding of the circle's center.

Formulas

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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 height of the segment, and d the height of the triangular portion.

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

Area

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The area of the circular segment is equal to the area of the circular sector minus the area of the triangular portion.

See also

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  • Weisstein, Eric W. "Circular segment". MathWorld.
  • Definition of a circular segment With interactive animation
  • Formulae for area of a circular segment With interactive animation
  • Circular segment calculator

Category:Circles