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The arc length, from the familiar geometry of a circle, is = The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of ):
The minor sector is shaded in green while the major sector is shaded white. A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. [1]
The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
Shape Figure ¯ ¯ Area rectangle area: General triangular area + + [1] Isosceles-triangular area: Right-triangular area: Circular area: Quarter-circular area [2]: Semicircular area [3]: Circular sector
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments. Circumference: the length of one circuit along the circle, or the distance around the circle. Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; or the length of such a line segment. This is the largest ...
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Circular segment - the part of the sector that remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary. Scale of chords; Ptolemy's table of chords; Holditch's theorem, for a chord rotating in a convex closed curve; Circle graph; Exsecant and excosecant