Circular segment

Segment of a circle ( circular segment ) called in the geometry of a partial surface of a circular area which is bounded by an arc and a chord.

Sizes of the circular segment:

  • α = angle subtended
  • B = arc
  • H = height of segment
  • R = radius
  • S = chord
  • A = area of ​​segment
  • M = center of circle

The area of ​​a circle segment can be calculated from the radius r and the corresponding central angle. They determined to the surface content of the corresponding circular sector and shown in the sketch isosceles triangle AMB. If the central angle less than 180 °, so you have to subtract this content area (sector area minus the triangle area). In a central angle about 180 °, the surface areas are to be added. If the central angle is exactly 180 °, the circle segment is a half circle, and the area of ​​the triangle is 0

In the formulas, the following table angle shall be placed in radians. The conversion of the measure of an angle from degrees to radians is done by the factor ( s radians).

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Special case of a semi-circle:

Arc (geometry) Inscribed angle#Theorem Wolfram Research
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