Theorem: The central angle
subtended
by two points on a circle is twice the inscribed angle
subtended by those points.

Try this Drag the orange dot at point P.
Note that the central angle
∠AOB is always twice the
inscribed angle ∠APB.

**The Central Angle Theorem** states that the measure of
inscribed angle (∠APB)
is always half the measure of the central angle ∠AOB.
As you adjust the points above, convince yourself that this is true.

This theorem only holds when P is in the major arc. If P is in the minor arc (that is, between A and B) the two angles have a different relationship. In this case, the inscribed angle is the supplement of half the central angle. As a formula: In other words, it is 180 minus what it would normally be.

- 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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