Because of the symmetrical nature of a circle, there are several relationships between angles inside circles.
Angle at the Centre
The angle made by an arc to the centre of a circle is equal to twice the angle made by the same arc at any point on the circumference.
(abbreviated to at centre = 2 × at circumference)
There are several possible positions for this situation:
Angle in a Semi-circle
Using the angle at centre property, it can be seen that the angle in a semi-circle is always 90º, a right angle.
(abbreviated to in a semi-circle is 90°)
AB is a diameter
Angles on the Same Arc
Angles on the same arc to the circumference, in the same segment, of a circle are equal.
(abbreviated to s on same arc are equal)
e.g. a = b = c