GCSE Maths · Topic guide
Circle theorem questions usually give a diagram: you must state the correct theorem, give a short reason, then calculate. Higher tier includes multi-step angle chasing; foundation may use fewer theorems but still expects clear vocabulary (‘angle at centre’, ‘angles in same segment’). Show the angle you’re using and avoid assuming lines are parallel or tangents unless marked or stated.
Worked examples & mini quiz
Key facts: angle in a semicircle is 90°; angle at centre = 2 × angle at circumference; angles in the same segment are equal; opposite angles in a cyclic quadrilateral sum to 180°; tangent ⟂ radius.
Example 1
Angle at centre
If angle at circumference = 35°, angle at centre on the same arc = 70°.
Example 2
Cyclic quadrilateral
Opposite angles sum to 180°. If one angle is 110°, the opposite is 70°.
Tap a row to reveal the answer — then start full adaptive practice for instant marking and feedback.
1. An angle inscribed in a semicircle is:
Correct: 90°Angle in a semicircle theorem.
2. The angle at the centre is:
Correct: Twice the angle at the circumference on the same arcCentral angle = 2 × inscribed angle on the same arc.
3. A tangent to a circle meets a radius at the point of contact at:
Correct: 90°Tangent ⟂ radius.
Opens StudyVector practice with your exam board context when you're signed in. Mixed sets may include a second weak topic from the same subject when data supports it.
Try one free question (no account)·Sign up for full adaptive practice
Stay inside the same syllabus — jump to another guide, then continue adaptive practice on your exam board.
GCSE Maths subject hub · Exam questions by topic · GCSE Maths predicted topics · Free question.
More: GCSE revision hub, GCSE Maths course.