The core circle theorems
Angle at the centre angle at the circumference (same arc); angle in a semicircle ; angles in the same segment are equal; opposite angles of a cyclic quadrilateral sum to ; a tangent meets a radius at .
Always give the proper reason
In "give a reason" parts you must name the theorem precisely, e.g. "the angle at the centre is twice the angle at the circumference".
Drawn from real examiner reports.
Giving an inadequate reason
Vague statements such as "it is double 54" or naming the wrong theorem score nothing.
Assuming a right angle that is not there
Treating an angle as 90° (or assuming a diameter) when the diagram does not justify it.
Misapplying the cyclic-quadrilateral theorem
Adding the two given angles and subtracting from 180 instead of using opposite angles.
Name the theorem you used
Marking the angle and quoting the exact theorem secures the reasoning mark.
Angle between a tangent and a radius?
is a cyclic quadrilateral. Angle . Find angle .
