ARC (GEOMETRY)

(Redirected from Circular arc)
A circular sector is shaded in green with length L along the circle's perimeter

In Euclidean geometry, a circular 'arc' is a closed segment of a differentiable curve in the two-dimensional plane; for example, an 'arc' is a segment of a circle. If the arc segment occupies a great circle (or great ellipse), it is considered a great-arc segment.
The length of an arc of a circle with radius r and subtending an angle heta,! (measured in radians) with the circle center—i.e., the 'central angle'—equals heta r,!. This is because
: rac{L}{mathrm{circumference}}= rac{ heta}{2pi}.,!
Substituting in the circumference
: rac{L}{2pi r}= rac{ heta}{2pi},,!
and solving for arc length, L, in terms of heta,! yields
:L= heta r.,!
For an angle lpha measured in degrees, the size in radians is given by
: heta= rac{lpha}{180}pi,,!
and so the arc length equals then
:L= rac{lphapi r}{180}.,!

Contents
See also
External links

See also



Arc length

Other meanings of arc

External links



Definition and properties of a circular arc With interactive animation

A collection of pages defining arcs and their properties, with animated applets Arcs, arc central angle, arc peripheral angle, central angle theorem and others.

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