# Arc

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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 and subtending an angle (measured in radians) with the circle center — i.e., the **central angle** — equals . This is because

Substituting in the circumference

and solving for arc length, , in terms of yields

An angle of degrees has a size in radians given by

and so the arc length equals

## See also

## 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.
- Weisstein, Eric W., "Arc" from MathWorld.

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