4PM1/02R Jun 2020, Question 5: Radians, Arcs and Sectors
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 8 marks
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The question, in short
Use the tangents from A to a circle of radius r with angle BOC = 2π/3 and shaded area 10 cm² to find r to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 8 marks
- 1Angle BOA = π/3, so AB = r tan(π/3) = √3 r
- 2Area of triangle OBA = ½r² tan(π/3); quadrilateral OBAC = √3 r²
- 3Area of sector = ½r² × 2π/3 = πr²/3
- 4Shaded area: √3 r² − πr²/3 = 10
- 5r² = 10/(√3 − π/3)
- 6r = 3.82
Answerr = 3.82
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