Circle Theorems

Angle at circumference is half that at the centre

Angles in the same segment are equal

Opposite angles in a cyclic quadrilateral add to 180°

The angle at the circumference of a semicircle is 90°

The angle between a tangent and a radius is 90°

The perpendicular from the centre of a circle to a chord bisects the chord.

Alternate Segment Theorem-The angle between a tangent and a chord is equal to the angle in the alternate segment.

Tangents meeting at the same point are the same length