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Circle theorems

Circle theorems for A Level Philosophy AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Philosophy
  • Foundation
  • Spec N11 · N16 · N20
  • 11 min read
  • 7 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.
The examiner marks the working, so a correct answer with no method still drops marks.
4 rows

The circle theorems reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
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
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left
Row 4 column 1
Row 4 column 2
×10\times 10 moves every digit one column left

Learning

3 boxes
5 steps

How to work with circle theorems

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
  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: 49=7\sqrt{49} = 7
3 rules

Key facts: Circle theorems

Practise the routine version until it is automatic, then move to the multi-step questions.
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.

  • 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.
    34×25\frac{3}{4} \times \frac{2}{5}
5 steps

How to work with circle theorems

The examiner marks the working, so a correct answer with no method still drops marks.
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: 49=7\sqrt{49} = 7

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Examples

2 boxes
1 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.
4 marks · worked

Practice question 7: ≈160\approx 160

The examiner marks the working, so a correct answer with no method still drops marks.

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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 A Level Philosophy AQA Foundation paper?
Yes — it sits in the Sources and evidence strand.