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Circle theorems

Circle theorems for A Level Philosophy Edexcel Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • Edexcel
  • Philosophy
  • Higher
  • Spec R8 · R15
  • 14 min read
  • 7 revision boxes

Introduction

2 boxes
3 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.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
5 rows

The circle theorems reference table

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.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 3 column 4
Row 3 column 5

Learning

3 boxes
5 steps

How to work with circle theorems

Read the units in the question before you start; a converted unit is the most common slip.
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.
  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: a2+b2=c2a^2 + b^2 = c^2.
Answer: 49=7\sqrt{49} = 7
3 rules

Key facts: 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.

  • 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.
    a2+b2=c2a^2 + b^2 = c^2
3 steps

How to work with circle theorems

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: ≈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: 49=7\sqrt{49} = 7.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
1 marks · worked

Worked example: circle theorems

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: ×10\times 10 moves every digit one column left.
3 marks · worked

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

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: ≈160\approx 160.

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