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°

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".

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.

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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