circle theorems

Angles at the centre

Angles at the centre

Angle at the centre is twice the angle at the circumference

Angles in the same segment

Angles in the same segment are equal.

Angles a = a

Angle in a semicircle

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

What is a cyclic quadrilateral?

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

Tangents

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.

Chords

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

The alternate segment theorem

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

Two Tangent Theorem

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