How to Identify Arcs and Central Angles
A circle’s central angles and the arcs that they cut out are part of many circle proofs. They also come up in many area problems. The following figure shows how an angle and an arc are interrelated.
- Arc: An arc is simply a curved piece of a circle. Any two points on a circle divide the circle into two arcs: a minor arc (the smaller piece) and a major arc (the larger)—unless the points are the endpoints of a diameter, in which case both arcs are semicircles.
Note that to name a minor arc, you use its two endpoints; to name a major arc, you use its two endpoints plus any point along the arc.
- Central angle: A central angle is an angle whose vertex is at the center of a circle. The two sides of a central angle are radii that hit the circle at the opposite ends of an arc—or as mathematicians say, the angle intercepts the arc.
The measure of an arc is the same as the degree measure of the central angle that intercepts it.