## arc

### In mathematics, an arc is a segment of a circle

In mathematics, an arc is a segment of a circle. It is defined as the curved path between two points on the circumference of a circle. The two points on the circle that define the arc are called the endpoints of the arc.

Arcs can be measured in terms of their length or angle. The length of an arc is proportional to the measure of the central angle that subtends it. More formally, if the central angle is expressed in radians, then the length of the arc can be calculated using the formula:

Arc length = r * θ

where r is the radius of the circle and θ is the measure of the central angle in radians. If the central angle is expressed in degrees, then the formula becomes:

Arc length = (π * r * θ) / 180

Arcs can be classified into different types based on their measure. A minor arc is an arc that spans less than 180 degrees, while a major arc spans more than 180 degrees. A semicircle is a special type of arc that spans exactly 180 degrees, creating a half-circle shape.

Arcs are used in various branches of mathematics, including trigonometry, geometry, and calculus. They play a role in calculating distances and angles, as well as in solving problems related to circles and circular motion.

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