Arc (geometry)

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


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


and so the arc length equals then

L=frac{alphapi r}{180}.,!

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