Circle theorem
- Identify the theorem.
- Mark equal radii or angles.
- Use the theorem to calculate the missing angle.
Answer: Opposite angles in a cyclic quadrilateral add to 180°
📐 Geometry & Measures
Circle theorems
Learn circle theorems with a GCSE-style explanation, help guide, worked example, practice question and flashcards.
Global XP
Level 10 / 100 XP
1. Explanation
Key idea
- Circle theorems is part of geometry and appears often in KS3–GCSE maths.
- Circle theorems give fixed angle relationships in circles.
- Use the worked model, help guide, interactive question and flashcards to practise circle theorems until the steps feel automatic.
Real-life examples
- Shopping, sport, travel, science, design and everyday decisions all use this skill.
2. Visual
Circle theorems learning map
Understand the key idea → follow the help guide → practise a question → check your method → build speed with flashcards.
3. Help guide
How to tackle Circle theorems
- Learn the rule: Circle theorems give fixed angle relationships in circles.
- Worked model: Identify the theorem. Mark equal radii or angles. Use the theorem to calculate the missing angle.
- Try the interactive question without looking at the answer first.
- Use the flashcards to test the rule, the method and a common check.
4. Worked examples
Step-by-step working
5. Interactive questions
Try it yourself
What is the angle in a semicircle?
6. Flashcards
Master quick recall
Flip each card, then choose whether you know it or need more practice.
0 mastered
FrontRule for Circle theorems
BackCircle theorems give fixed angle relationships in circles.
FrontExample answer: What is the angle in a semicircle?
BackThe angle in a semicircle is always a right angle, so it is 90°.
FrontCommon check for Circle theorems
BackCheck units/notation, compare with an estimate, and make sure the answer matches the question.
7. Finish
Complete this topic
When you have read the examples, tried the question and reviewed flashcards, claim your topic completion XP.