DfE statement A16 · Algebra

Equation of a circle and its tangent

Higher onlyNon-calculator

Equation of a circle and its tangent is content statement A16 of the DfE GCSE mathematics subject content, in the algebra area. It is Higher tier only, and it is examined without a calculator. Below is what the specification actually requires, the 3 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: "Recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point." (statement A16). 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 A16

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

Reading x² + y² = 25 as a circle of radius 25. The right-hand side is r², so the radius is 5.
Giving the tangent the same gradient as the radius. The tangent is perpendicular to the radius at the point of contact, so its gradient is the negative reciprocal.
Finding the gradient correctly and then failing to substitute the given point to find the intercept.

Sample questions (10 of 30)

A16 · Equation of a circle and its tangentQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Algebra

A16

Advanced

A circular running track is modelled on a grid whose centre is the origin, where each unit represents 1 metre. A floodlight at the point (30, 40) stands on the edge of the track. A second floodlight stands on the edge of the track at the point (0, k), where k is positive. Work out the value of k.

💡 Hints:

Higher worksheet Higher algebra practice

Nearby statements

A1Algebraic notation A2Substitution into formulae A3Expressions, equations, formulae, identities and inequalities

Questions people ask

Is equation of a circle and its tangent on Foundation or Higher?

Higher only. Foundation papers do not ask for it.

Can I use a calculator for equation of a circle and its tangent?

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.

What is the single most common mistake here?

Reading x² + y² = 25 as a circle of radius 25. The right-hand side is r², so the radius is 5.

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 Algebra at Foundation or at Higher.