A Level Maths: Circle Geometry Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Straight Line Geometry — essential for tangent and chord equations
- Quadratic Equations — completing the square is needed to find centre and radius from expanded form
- Surds — surd answers are common when calculating exact distances
A Level Maths circle geometry builds on Straight Line Geometry, focusing on circles in the coordinate plane. You learn to recognise, manipulate, and solve problems involving the equation of a circle, and to use key geometric properties to find tangents, chords, and special points. The skills here recur throughout A Level — in Vectors, Trigonometry, and curve sketching.
You work with the standard form $(x – a)^2 + (y – b)^2 = r^2$ and the expanded form $x^2 + y^2 + 2fx + 2gy + c = 0$, converting between them using completing the square to find the centre and radius. You use three core properties: the angle in a semicircle is a right angle, the perpendicular from the centre to a chord bisects the chord, and the radius drawn to the point of contact is perpendicular to the tangent. These let you find tangent equations at specific points, intersection points of lines with circles, and the equation of a circumcircle of a triangle from its vertices.
Circle geometry is part of the Pure Maths strand of A Level Maths and is essential revision content for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: when completing the square to find the centre, remember the centre coordinates have the opposite sign to the numbers inside the brackets — $(x – 3)^2$ has centre $x = +3$, not $-3$; the radius is $\sqrt{r^2}$, not $r^2$ itself; check the discriminant of a substituted line-circle equation to determine the number of intersection points ($0$, $1$ tangent, or $2$ chord); and for the tangent at a point, the gradient is the negative reciprocal of the radius gradient at that point.