Relationship Between Central Angle and Inscribed Angle

Central angle = Angle subtended by an arc of the circle from the center of the circle.
Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle. Also called circumferential angle and peripheral angle.
 

Figure below shows a central angle and inscribed angle intercepting the same arc AB. The relationship between the two is given by
 

$\alpha = 2\theta \, \text{ or } \, \theta = \frac{1}{2}\alpha$

 

if and only if both angles intercepted the same arc. In the figure below, θ and α intercepted the same arc AB.
 

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