In addition to the circle theory already discussed, it is necessary to memorise the following so that we can identify them in problems. Do be aware that questions will not typically tell you which circle theory to use. You need to know all of them so that you can apply them in any questions where they are relevant.
CT3. The angle a chord subtends at the centre of a circle is twice as large as the angle it subtends at the circumference.
CT4. Within the same segment, any angles subtended by the same chord are equal.
CT5. The opposite angles of a cyclic quadrilateral sum to 180 degrees
CT6.1. For any circle, the angle between a tangent and a chord through the point of contact of the tangent is equal to the angle made by the chord in the alternate segment.
CT 6.2. Each exterior angle of a cyclical quadrilateral is equal to the opposite interior angle. (This circle theory is not included in syllabus)