Central Angle

Definition: The angle subtended at the center of a circle by two given points on the circle.
Try this Drag any orange dot. Note that when moving the points A or B the angle at the center changes.

Given two points A and B, lines from them to center of the circle form the central angle AOB. The central angle is the smaller of the two at the center. It does not mean the reflex angle AOB. As you drag the points above, the angle will change to reflect this as it increases through 180°

Arcs and Chords

The two points A and B can be isolated points, or they could be the end points of an arc or chord. When they are the end points of an arc, the angle is sometimes called the "arc central angle".

Inscribed Angle

A similar concept is the inscribed angle. This is the angle subtended at a point on the circle by the two given points. See Inscribed Angle definition

The central angle is always twice the inscribed angle. See Central Angle Theorem.

Other circle topics


Equations of a circle

Angles in a circle