Because of the symmetrical nature of a circle, there are several relationships between angles inside circles.

Angle at Centre
Angle in a Semi-circle
Angles on same arc

LondonEyeBig.JPGAngle 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 Y10_Angles_in_Circles_01.gif at centre = 2 × Y10_Angles_in_Circles_01.gif 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 Y10_Angles_in_Circles_01.gif 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 Y10_Angles_in_Circles_01.gifs on same arc are equal)

e.g. a = b = c