Pass Functional Skills logo

Circle theorems

Circle theorems for GCSE Statistics Edexcel Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Statistics
  • Higher
  • Spec N12
  • 6 min read
  • 7 revision boxes

Introduction

2 boxes
1 min read

What is circle theorems?

Listen to this box

Transcript

A short spoken summary of circle theorems and where it is used.

A spoken walk-through of circle theorems before you read the notes.
Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: ×10\times 10 moves every digit one column left.
6 rows

The circle theorems reference table

Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing circle theorems laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 3 column 4
Row 3 column 5
Row 4 column 1
Row 4 column 2
×10\times 10 moves every digit one column left
Row 4 column 4
Row 4 column 5

Learning

3 boxes
5 steps

How to work with circle theorems

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
  1. Read the question and write down what is being asked for.
  2. Set out the working for circle theorems in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: ×10\times 10 moves every digit one column left
3 rules

Key facts: Circle theorems

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: ≈160\approx 160.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How circle theorems behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7
5 steps

How to work with circle theorems

Check the answer against an estimate before you move on, so a place-value slip is caught here.
The layout below is the one the mark scheme expects.

Diagram showing circle theorems laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for circle theorems in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: 49=7\sqrt{49} = 7

20 minutes

Get your predicted grade

Twenty questions gives you a predicted grade, your target, and the gap between them — plus the topics that close it fastest.
Get my predicted grade

Examples

2 boxes
3 marks · worked

Worked example: circle theorems

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ≈160\approx 160.
3 marks · worked

Practice question 7: a2+b2=c2a^2 + b^2 = c^2

Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing circle theorems laid out step by step

The same idea drawn out, so the method is visible.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
5,000+
Topics
10
Marking and solutions
Instant

Common questions

How many marks is circle theorems usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Statistics Edexcel Higher paper?
Yes — it sits in the Sources and evidence strand.