4PM1/02 Jun 2022, Question 4: Radians, Arcs and Sectors
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks
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The question, in short
Two radius-6 circles each pass through the other's centre, intersecting at A and B; find the exact shaded overlap area P in the form aπ − b√c.
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Solution · 7 marks
- 1O₁A = O₂A = O₁O₂ = 6, so triangle AO₁O₂ is equilateral
- 2Angle AO₁O₂ = π/3, so angle AO₁B = 2π/3
- 3Sector AO₁B (centre O₁) = (1/2) × 6² × 2π/3 = 12π
- 4Triangle AO₁B = (1/2) × 6² × sin(2π/3) = 9√3
- 5Segment = 12π − 9√3
- 6P = 2(12π − 9√3) = 24π − 18√3
AnswerP = 24π − 18√3
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