Circle theorems

Theorems are the different angle properties of circles. There are 7 theorems.

Subtend: angle created by two chords.

1. The angle at the centre is double the angle at the circumference.

2. The angles in the same segment are equal.

3. The opposite angles in a cyclic quadrilateral add up to 180°.

4. The angle at the circumference in a semicircle is a right angle.=

5a. The angle between a tangent and a radius is 90°.

5b. Tangents which meet at the same point are equal in length.

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

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