Circle Theorems

The angle subtended at the centre of a circle (a) is twice the angle subtended at the circumference (b) within the same segment

Angles subtended by a chord in the same segment of the circle are equal

Opposite angles of a cyclic quadrilateral add up to 180 degrees -         A+C = 180 degrees - B+D = 180 degrees

The angle in a semi-circle is 90 degrees

The perpendicular bisector of any chord passes through the centre of the circle (0)

From any point outside a circle, two tangents to the circle can be drawn and they are of equal length: PA = PB

The angle between a tangent and the radius drawn to the point of contact is 90 degrees

The angle between a tangent and a chord through the point of contact is equal to the angle subtended by the chord in the alternate segment