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 the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center. Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Theaetetus dealing with spatial relationships. ... In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the centre. ... A secant line of a curve is a line that intersects two (or more) points on the curve. ... A chord of a curve is a geometric line segment whose endpoints both lie on the curve. ...

Formulae

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

Let R be the radius of the circle, c the chord length, s the arc length, h the height of the segment, and d the height of the triangular portion. The area of the circular segment is equal to the area of the circular sector minus the area of the triangular portion. From [1] This image is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. ... RADIUS (Remote Authentication Dial In User Service) is an Authentication, Authorization and Accounting (AAA) protocol for applications such as network access or IP mobility. ... In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the centre. ... In general English usage, length (symbol: l) is but one particular instance of distance – an objects length is how long the object is – but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth) is... Height is a measurement of the distance from the bottom to the top of something which is upright. ... A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments. ... This article explains the meaning of area as a physical quantity. ... A circular sector (also circle sector) is the portion of a circle enclosed by two radii and an arc. ...

The radius is 

The arc length is 

The area is 

Derivation of the area formula

The area of the circular sector is 

If we bisect angle θ, and thus the triangular portion, we will get two triangles with the area or File links The following pages link to this file: Circular segment Categories: User-created public domain images ...

Since the area of the segment is the area of the sector decreased by the area of the triangular portion, we have

According to trigonometry, sinxcosx = 2sinxcosx = 2sinx, therefore

The area is therefore:

See also

• Circular sector

A circular sector (also circle sector) is the portion of a circle enclosed by two radii and an arc. ...

External links

• MathWorld's definition of "circular segment" (http://mathworld.wolfram.com/CircularSegment.html)