Homeschool Guide: These lesson plans are a guide for parents. Content may contain errors — always cross-reference with official exam board specifications.

G10: Circle Theorems

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: Circle Theorems

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

3 quick questions to activate prior knowledge about circle theorems. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: G10.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Circle Theorems. Goal: by the end you can points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc), using the method shown step by step. Connects to circle parts (G9) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Circle Theorems is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  1. What is asked? Points
  2. Recall knowledge: Centre = 2 × circumference (same arc) · semicircle angle = 90°; Same segment: angles equal · cyclic quad: opposite angles sum to 180°
  3. Apply: Angle at centre = 2 × angle at circumference = 110°
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 110°

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Break down: Separate parts?
  2. Solve each: x + x + 40 = 180 → x = 70 → 70° and 110°
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the supplementary rule, A1 for both. Opposite angles in cyclic quadrilaterals ALWAYS sum to 180°.
Worked Example 3: Data/Application

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using circle theorems
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Centre = 2 × circumference (same arc) · semicircle angle = 9 work this way?"
A: Analogy: "Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Circle Theorems in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to G1-geometric-notation / G11-coordinate-geometry
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on circle theorems, summarise 100 words

Plenary (5 mins)

Label the Diagram

Unlabelled diagram - write all parts in 1 min

Assessment Criteria

Lesson 2: Core Concepts: Circle Theorems

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from last lesson on circle theorems. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: G10.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Circle Theorems. Goal: by the end you can points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc), using the method shown step by step. Connects to circle parts (G9) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Circle Theorems is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  1. What is asked? Points
  2. Recall knowledge: Centre = 2 × circumference (same arc) · semicircle angle = 90°; Same segment: angles equal · cyclic quad: opposite angles sum to 180°
  3. Apply: Angle at centre = 2 × angle at circumference = 110°
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 110°

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Break down: Separate parts?
  2. Solve each: x + x + 40 = 180 → x = 70 → 70° and 110°
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the supplementary rule, A1 for both. Opposite angles in cyclic quadrilaterals ALWAYS sum to 180°.
Worked Example 3: Data/Application

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using circle theorems
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Centre = 2 × circumference (same arc) · semicircle angle = 9 work this way?"
A: Analogy: "Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Circle Theorems in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to G1-geometric-notation / G11-coordinate-geometry
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on circle theorems, summarise 100 words

Plenary (5 mins)

Label the Diagram

Unlabelled diagram - write all parts in 1 min

Assessment Criteria

Lesson 3: Application: Circle Theorems

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from last lesson on circle theorems. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: G10.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Circle Theorems. Goal: by the end you can points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc), using the method shown step by step. Connects to circle parts (G9) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Circle Theorems is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  1. What is asked? Points
  2. Recall knowledge: Centre = 2 × circumference (same arc) · semicircle angle = 90°; Same segment: angles equal · cyclic quad: opposite angles sum to 180°
  3. Apply: Angle at centre = 2 × angle at circumference = 110°
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 110°

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Break down: Separate parts?
  2. Solve each: x + x + 40 = 180 → x = 70 → 70° and 110°
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the supplementary rule, A1 for both. Opposite angles in cyclic quadrilaterals ALWAYS sum to 180°.
Worked Example 3: Data/Application

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using circle theorems
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Centre = 2 × circumference (same arc) · semicircle angle = 9 work this way?"
A: Analogy: "Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Circle Theorems in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to G1-geometric-notation / G11-coordinate-geometry
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on circle theorems, summarise 100 words

Plenary (5 mins)

Exam Question Speed Round

5 quick questions, 1 min each. Mark together.

Assessment Criteria

Lesson 4: Exam Practice: Circle Theorems

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from last lesson on circle theorems. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: G10.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Circle Theorems. Goal: by the end you can points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc), using the method shown step by step. Connects to circle parts (G9) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Circle Theorems is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  1. What is asked? Points
  2. Recall knowledge: Centre = 2 × circumference (same arc) · semicircle angle = 90°; Same segment: angles equal · cyclic quad: opposite angles sum to 180°
  3. Apply: Angle at centre = 2 × angle at circumference = 110°
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 110°

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Break down: Separate parts?
  2. Solve each: x + x + 40 = 180 → x = 70 → 70° and 110°
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the supplementary rule, A1 for both. Opposite angles in cyclic quadrilaterals ALWAYS sum to 180°.
Worked Example 3: Data/Application

Q: A cyclic quadrilateral has angles x and (x + 40)° opposite each other. Find both.

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using circle theorems
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Centre = 2 × circumference (same arc) · semicircle angle = 9 work this way?"
A: Analogy: "Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Circle Theorems in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Points A, B, C on a circle. Angle ABC = 55°. Find the angle at the centre AOC (subtended by the same arc).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to G1-geometric-notation / G11-coordinate-geometry
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on circle theorems, summarise 100 words

Plenary (5 mins)

Exam Question Speed Round

5 quick questions, 1 min each. Mark together.

Assessment Criteria

📝 Mark Scheme Guidance

How examiners mark G10: Read the command word carefully — State = one word/phrase (1 mark), Describe = pattern or detail (2 marks), Explain = reason with "because" (2–3 marks), Compare = similarities AND differences, Evaluate = both sides + conclusion. Method marks are awarded for correct working even if the final answer is wrong. Always show your working — unexplained answers score zero for AO2.

Success on G10 questions: Underline the command word, count the marks (one mark per point expected), and answer in the format the command word demands.

Board Notes & Revision Links

This lesson is examined by: AQA 8300 | Edexcel 1MA1 | OCR J560 | Eduqas C300 | CCEA M-units. Tier and paper details vary - always check your board's current specification.

Follow-up revision: G10-circle-theorems on GCSE Revise (notes, flashcards and auto-graded target tests for this exact topic).

📐 Reference Diagram

x y y = x² Origin (0,0)

✏️ Draw-Along Instructions

Parent/teacher: Draw the shape using a ruler. Label all sides with their lengths. Mark equal angles with arcs. Add any parallel-line arrows. Write the formula you will use inside the shape.

Display the reference diagram (or draw it live) while pupils copy. Check each label as it is added.

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)