Fiducia TogetherCircle theorems
A set of rules about angles in circles. Higher tier, and questions expect the rule named.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
The standard set: the angle at the centre is twice the angle at the circumference; angles in the same segment are equal; the angle in a semicircle is 90°; opposite angles in a cyclic quadrilateral sum to 180°; a tangent meets a radius at 90°; tangents from a point are equal; and the alternate segment theorem.
Where it applies
Higher tier maths.
How it works
Each theorem lets you deduce one angle from another, and questions chain two or three together.
How to use it in your work
NAME the theorem you use. Marks are explicitly for reasons — "angles in the same segment are equal" earns the mark, "because it looks the same" does not.
Mark the diagram as you go. Every angle you find is evidence for the next step.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.