Circle theorems (including intersecting chords)

Angles in the same segment are equal

The angle in a semicircle is 90^o

The angle at the circumference is half the angle at the centre

Opposite angles in a cyclic quadrilateral sum to 180^o

The tangent is perpendicular to the radius

Tangents from the same point are equal in length

Two chords intersect inside the circle
ab = cd

Two chords intersect outside the circle
ab = cd

A chord and tangent intersect outside the circle
a² = bc