circle theorems

Angle at the centre is twice the angle at the circumference

Angles in the same segment are equal.

Angles a = a

The angle in a semicircle is 90° or a right angle

A cyclic quadrilateral is a quadrilateral drawn inside a circle. Every corner of the quadrilateral must touch the circumference of the circle.

There are two circle theorems involving tangents.

1. The angle between a tangent and a radius is 90°.

2. Tangents which meet at the same point are equal in length.

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

The angle between a tangent and a chord is equal to the angle in the alternate segment.

if two tangent segments are drawn to one circle from the same external point, then they are congruent.