Arc

Definition

An arc is a portion of the circumference of a circle. It is defined by two points on the circle and the continuous part of the circle between them.

5 Must Know Facts For Your Next Test

1. The measure of an arc is given in degrees or radians and corresponds to the central angle that subtends it.
2. In a unit circle, the length of an arc corresponding to an angle $\theta$ (in radians) is equal to $\theta$ itself.
3. A minor arc is an arc that measures less than 180 degrees, while a major arc measures more than 180 degrees.
4. The formula for the length of an arc in a circle with radius $r$ and central angle $\theta$ (in radians) is $L = r\theta$.
5. Arcs can be used to define sectors and segments in circles, which are important for calculating areas and other properties.

Review Questions

• What is the relationship between the length of an arc and its central angle in a unit circle?
• How do you differentiate between a minor arc and a major arc?
• If given a radius and central angle in radians, how would you calculate the length of an arc?

Related terms

Central Angle: An angle whose vertex is at the center of a circle and whose sides intersect the circle.

Radian: A measure of angle based on the radius of a circle; one radian equals approximately $57.2958^{\circ}$.

Sector: The region enclosed by two radii of a circle and their intercepted arc.