Inscribed Angles and Central Angles
We will first look at some definitions.
An inscribed angle has its vertex on the circle. ∠ABC, in the diagram below, is called an inscribed angle or angle at the circumference. The angle is also said to be subtended by (i.e. opposite to) arc ADC or chord AC
inscribed angle
Property: The inscribed angles subtended by the same arc are equal.
inscribed angles
∠x = ∠y because they are subtended by the same arc AEC.
Property: Inscribed angle in a semicircle is 90˚.
angle in semicircle
POQ is the diameter. ∠PAQ = ∠PBQ = ∠PCQ = 90˚.
A central angle has its vertex is at the centre of the circle. In the diagram below, ∠AOC is called a central angle.
Central Angle
Property: Central angles subtended by arcs of the same length are equal.
Central Angles
∠ x = ∠ y because arc AB = arc CD
