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Circle theorems

Circle theorems for GCSE Maths Edexcel Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Maths
  • Foundation
  • Spec R18
  • 6 min read
  • 10 revision boxes

Introduction

2 boxes
3 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.
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.
2 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.
Worth knowing: ×10\times 10 moves every digit one column left.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 2 column 4

Learning

6 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: ≈160\approx 160.
  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: ≈160\approx 160
3 rules

Key facts: Circle theorems

Read the units in the question before you start; a converted unit is the most common slip.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
3 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.
  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: ×10\times 10 moves every digit one column left.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Circle theorems

Work through the method one line at a time and write down what changes at each step.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
4 steps

How to work with circle theorems

The specification wording is precise here, and the mark scheme follows that wording exactly.
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: a2+b2=c2a^2 + b^2 = c^2.
  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.
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: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Circle theorems

Read the units in the question before you start; a converted unit is the most common slip.

  • Rule 1

    How circle theorems behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

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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.
1 marks · worked

Practice question 10: 49=7\sqrt{49} = 7

This idea appears again in the higher-mark questions, so it is worth over-learning.

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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 Maths Edexcel Foundation paper?
Yes — it sits in the Sources and evidence strand.