Central Angle Theorem

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.

Exception

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.

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs

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