4MA1/2HR Jan 2021, Question 20: Area of a Sector
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
Points A, B, C lie on a circle centre O with angle ABC = 75° and shaded segment area 200 cm²; find the radius to 3 significant figures.
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Solution · 5 marks
- 1Angle at the centre is twice the angle at the circumference: AOC = 2 × 75 = 150°
- 2Sector = 150/360 × πr²; triangle AOC = ½ × r² × sin 150° = 0.25r²
- 3Segment: (150/360)πr² − 0.25r² = 200, so 1.0589…r² = 200
- 4r² = 188.8…, so r = 13.7
Answer13.7
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