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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 topicsGeneral
Angles in a circleArcs
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