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Circle theorems

Circle theorems for GCSE Business Studies AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Business Studies
  • Spec G11 · G18
  • 6 min read
  • 6 revision boxes

Introduction

2 boxes
2 min read

What is circle theorems?

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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.
Worth knowing: ≈160\approx 160.
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: x2+5x+6=0x^2 + 5x + 6 = 0.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7

Learning

2 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: 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.
  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: ×10\times 10 moves every digit one column left
2 rules

Key facts: Circle theorems

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

  • 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.
    a2+b2=c2a^2 + b^2 = c^2

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Examples

2 boxes
4 marks · worked

Worked example: 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: x2+5x+6=0x^2 + 5x + 6 = 0.
1 marks · worked

Practice question 6: ≈160\approx 160

The specification wording is precise here, and the mark scheme follows that wording exactly.

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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 Business Studies AQA paper?
Yes — it sits in the Sources and evidence strand.