# Arc

### circle angle length circumference

An arc is a segment of a **curve**, most often a **circle**. In the strictest definition, an arc is a segment of a curve in a **plane**. Examples include segments of geometrical forms such as circles, ellipses, and parabolas, as well as irregular arcs defined by analytical functions.

Arcs of circles can be classified by size. A minor arc is one whose length is shorter than one-half of the circumference of a circle. A major arc is one whose length is longer than one half of the circumference of a circle. An arc whose length is exactly one-half of the circumference of the circle is simply called a semi-circle. The line connecting the endpoints of a major arc or minor arc is called a chord.

Angles subtended by circles can be classified by the location of the vertex. One important type of **angle** has the vertex located at the circumference. An angle whose vertex is at the center of the circle is called a central angle. Each specific central angle is subtended by only one arc, but each arc subtends infinitely many angles.

An arc of a circle can be measured by length along the circumference, or in terms of the angle subtended by the arc. A **theorem** of **geometry** states that the measure of the central angle of the circle is the measure of corresponding arc. If the arc lies on a circle of radius *r* and subtends a central angle (*L*A) measured in degrees, then the length of the arc is given by *b* = 2π*r*(*L*A/360).

In the case of irregular arcs, the length can be determined using **calculus** and differential geometry.

Kristin Lewotsky

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