alternate segment

Think of a chord in a circle. This is shown on the diagram by the line connecting point D and point C on the circle.

When a tangent meets a chord on a circumference, an angle is formed between the tangent and the chord. This has been labelled a.

The chord divides the circle into two segments. One segment is between the chord and the tangent. The other segment in the circle is the alternate segment.

An angle that is formed in the alternate segment by the two ends of the chord is equal to angle a. Therefore, in the diagram, angle b is equal to angle a.