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In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference 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 $theta,!$ (measured in radians) with the circle center — i.e., the central angle — equals $theta\; r,!$. This is because

- $frac\{L\}\{mathrm\{circumference\}\}=frac\{theta\}\{2pi\}.,!$

Substituting in the circumference

- $frac\{L\}\{2pi\; r\}=frac\{theta\}\{2pi\},,!$

and solving for arc length, $L$, in terms of $theta,!$ yields

- $L=theta\; r.,!$

For an angle $alpha$ measured in degrees, the size in radians is given by

- $theta=frac\{alpha\}\{180\}pi,,!$

and so the arc length equals then

- $L=frac\{alphapi\; r\}\{180\}.,!$

- 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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Last updated on Saturday October 11, 2008 at 01:23:12 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday October 11, 2008 at 01:23:12 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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