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**°**)

e.g.

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