GCSE · Maths
Circle theorems
What is circle theorems?
GCSE Maths circle theorems are a closed set of geometric rules about angles in a circle. The seven examinable rules: angle at the centre = 2× angle at the circumference; angle in a semicircle = 90°; angles in the same segment are equal; opposite angles in a cyclic quadrilateral sum to 180°; tangent meets radius at 90°; alternate segment theorem; tangents from an external point are equal.
Where it appears in exams
- Find an angle using 'angle at centre is twice the angle at circumference'.
- Prove a quadrilateral is cyclic by showing opposite angles sum to 180°.
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