| Lesson Plan |
| Grade: |
Date: 25/02/2026 |
| Subject: Additional Mathematics |
| Lesson Topic: Solve problems involving the intersection of two circles, including finding points of intersection, the equation of a common chord and deciding whether two circles intersect, touch or do not meet |
Learning Objective/s:
- Describe the standard and general forms of a circle equation.
- Determine the relative position of two circles using the centre distance and radii.
- Derive the equation of the common chord (radical line) by subtracting the two circle equations.
- Solve for the coordinates of intersection points of two circles.
- Apply the method to classify circles as intersecting, touching externally/internally, or separate.
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Materials Needed:
- Projector or interactive whiteboard
- Printed worksheet with practice questions
- Graph paper, compasses and rulers
- Scientific calculators
- Prepared digital slides showing circle diagrams
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Introduction:
Begin with a quick visual of two overlapping circles on the screen to spark curiosity about where they meet. Recall the equation of a circle and how to identify its centre and radius. Explain that today’s success criteria are to classify the position of two circles and to compute their intersection points or common chord.
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Lesson Structure:
- Do‑now (5') – short recall quiz on circle equations and centre‑radius identification.
- Mini‑lecture (10') – derive standard to general form, introduce distance d and the six relative‑position cases.
- Interactive demonstration (12') – use geometry software to illustrate each case and derive the common chord equation by subtraction.
- Guided practice (15') – work through Worked Example 1 as a class, filling each algebraic step together.
- Pair activity (10') – solve Worked Example 2, decide the circles’ relationship and verify the intersection points.
- Independent practice (15') – students attempt the three practice questions while the teacher circulates for support.
- Exit ticket (5') – each student writes one sentence summarising how to decide the relationship of two circles.
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Conclusion:
Recap the key steps: compute the centre distance, compare with the sum and difference of radii, obtain the common chord, and solve for intersection coordinates. Collect exit tickets to check understanding, and assign the remaining practice questions as homework for reinforcement.
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