Circles have different angle properties described by different circle theorems. Circle theorems are used in geometric proofs and to calculate angles.

Part of

The angle subtended by an arc at the centre is twice the angle subtended at the circumference.

More simply, the angle at the centre is double the angle at the circumference.

Calculate the missing angles and .

=

=

Let angle OGH = and angle OGK = .

Angle OGH ( ) = angle OHG because triangle GOH is an isosceles. Lengths OH and OG are both radii.

Angle OGK ( ) = angle OKG because triangle GOK is also isosceles. Lengths OK and OG are also both radii.

Angle GOH = (because angles in a triangle add up to 180°)

Angle GOK = (because angles in a triangle add up to 180°)

Angle JOH = (because angles on a straight line add up to 180° )

Angle JOK = (because angles on a straight line add up to 180°)

The angle at the centre KOH ( ) is double the angle at the circumference KGH ( ).