
Central Angle Theorem
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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