Editing Inscribed angle (section)

===Statement===

[[File:ArcCapable.gif|thumb|class=skin-invert-image|For fixed points {{mvar|A}} and {{mvar|B}}, the set of points ''M'' in the plane, for which the angle {{math|∠''AMB''}} is equal to&nbsp;''α'', is an arc of a circle. The measure of {{math|∠''AOB''}}, where {{mvar|O}} is the center of the circle, is&nbsp;{{math|2''α''}}.]]

The inscribed angle theorem states that an angle {{mvar|θ}} inscribed in a circle is half of the central angle {{math|2''θ''}} that [[intercepted arc|intercepts]] the same [[arc (geometry)|arc]] on the circle.  Therefore, the angle does not change as its [[vertex (geometry)|vertex]] is moved to different positions on the same arc of the circle.