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GCSE Maths: Circle Theorems

Apply circle theorems to find missing angles and prove geometric statements. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

GeometryFoundation & HigherAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on circle theorems, and what each one is really asking.

Identify and apply the 7 key circle theorems
Provide rigorous geometric reasons for angle calculations
Spot isosceles triangles formed by radii
Prove circle theorems algebraically

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • Not learning the exact theorem names (e.g. writing 'bowtie angles' instead of 'angles in same segment')
  • Assuming a quadrilateral is cyclic when one vertex is at the centre (all 4 must be on the circumference!)
  • Missing hidden isosceles triangles formed by two radii
  • Halving the wrong angle for the centre/circumference theorem

Circle Theorems questions students ask

Is Circle Theorems on the Foundation paper?

Yes. Circle Theorems appears at both Foundation and Higher tier, though Higher papers take it further.

What should I know before starting Circle Theorems?

It builds on Angle facts and Properties of triangles and quadrilaterals. If those feel shaky, practise them first — Circle Theorems questions assume them.

What is the most common mistake in Circle Theorems?

Not learning the exact theorem names (e.g. writing 'bowtie angles' instead of 'angles in same segment').

Which exam boards cover Circle Theorems?

All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.