DfE statement G10 · Geometry and measures

Circle theorems

Higher onlyNon-calculator

Circle theorems is content statement G10 of the DfE GCSE mathematics subject content, in the geometry area. It is Higher tier only, and it is examined without a calculator. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results." (statement G10). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement G10

Tier

Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

Halving the angle at the centre instead of doubling the angle at the circumference — the angle at the centre is twice the one at the circumference.
Applying 'angles in the same segment are equal' to angles that sit in different segments.
Using the alternate segment theorem with the wrong pair: the angle between the tangent and the chord equals the angle in the alternate segment, not the adjacent one.
Giving the answer with no theorem named. These questions are marked on the reasons as much as the numbers.

Sample questions (10 of 30)

G10 · Circle theoremsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Geometry and measures

G10

Expert

A student is proving that opposite angles of a cyclic quadrilateral ABCD sum to 180°, letting a = angle DAB and c = angle BCD, and using the fact that the angle at the centre is twice the angle at the circumference. She has already written: 'By the angle at the centre theorem, the reflex angle BOD equals 2a and the non-reflex angle BOD equals 2c.' Which statement must come immediately after this one in a correct proof?

💡 Hints:

Higher worksheet Higher geometry and measures practice

Nearby statements

G1Geometric terms, notation and diagrams G2Ruler and compass constructions and loci G3Angle facts, parallel lines and polygons

Questions people ask

Is circle theorems on Foundation or Higher?

Higher only. Foundation papers do not ask for it.

Can I use a calculator for circle theorems?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

Do I have to name the circle theorem I used?

Yes, if the question asks you to give reasons — and most of them do. Write the theorem in words, not as 'circle theorem 4': 'the angle in a semicircle is 90°', 'opposite angles in a cyclic quadrilateral add to 180°'. Circle theorems are Higher tier only.

What is the single most common mistake here?

Halving the angle at the centre instead of doubling the angle at the circumference — the angle at the centre is twice the one at the circumference.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Geometry and measures at Foundation or at Higher.