The measure of a central angle (whose vertex is in the center of the circumference), is equal to the amplitude of its corresponding arc. On the other hand the measure of an inscribed angle is equal to half of the measure of the arc comprised between its sides.

**Any angle inscribed on a circle has half the measure that a central angle with the same arc.**

Created with GeoGebra by Vitor Nunes

You can move points A and B along the circumference. Thus you will verify that the angle `beta` always has half the value of the `alpha` angle.

You can move point C along the ACB arc and check that the angle `beta` always has the same value!

Inscribed angle theorems exist for ellipses, hyperbolas and parabolas, too. The essential differences are the measurements of an angle.