Central Angle Theorem - Math Open Reference

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.

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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

Recall that the inscribed angle is undefined in the minor arc. (See Inscribed Angle). As a result, under this condition this theorem does not hold either. Move point P into the minor arc and see what happens.

Other circle topics

Other circle topics

General

Angles in a circle

Arcs