Central Angle Theorem - Math Open Reference (original) (raw)

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 supplementof half the central angle. As a formula: In other words, it is 180 minus what it would normally be.