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Circle theorems

Circle theorems for GCSE Philosophy Edexcel Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • Edexcel
  • Philosophy
  • Foundation
  • Spec S20
  • 12 min read
  • 6 revision boxes

Introduction

2 boxes
1 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.
Practise the routine version until it is automatic, then move to the multi-step questions.
3 rows

The circle theorems reference table

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
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
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 1 column 4
Row 2 column 1
Row 2 column 2
≈160\approx 160
Row 2 column 4
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7
Row 3 column 4
Row 4 column 1
Row 4 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 4 column 4

Learning

2 boxes
4 steps

How to work with circle theorems

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.
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: ×10\times 10 moves every digit one column left.
Answer: a2+b2=c2a^2 + b^2 = c^2
3 rules

Key facts: Circle theorems

The examiner marks the working, so a correct answer with no method still drops marks.
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.
    ≈160\approx 160

  • Rule 2

    How circle theorems behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

  • Rule 3

    How circle theorems behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
3 marks · worked

Worked example: circle theorems

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

Practice question 6: ×10\times 10 moves every digit one column left

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

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