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Circle theorems

Circle theorems for A Level Environmental Science OCR: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • OCR
  • Environmental Science
  • Spec P20 · P6
  • 11 min read
  • 6 revision boxes

Introduction

2 boxes
1 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.
This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
4 rows

The circle theorems reference table

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: 49=7\sqrt{49} = 7.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}

Learning

2 boxes
5 steps

How to work with 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.
  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: ×10\times 10 moves every digit one column left.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Circle theorems

Sketch the shape even when the question does not ask for one — it makes the next step obvious.

  • 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.
    ×10\times 10 moves every digit one column left

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Examples

2 boxes
3 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.
2 marks · worked

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

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.

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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 Environmental Science OCR paper?
Yes — it sits in the Sources and evidence strand.