4MA1/2HR Jan 2023, Question 14: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks
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The question, in short
Circle centre O with radius 8.5 cm; points A, B, C on circle, angle ABC = 132°. Find perimeter of shaded major sector AOC, to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1Angle at the centre is twice the angle at the circumference, so angle AOC = 2 × 132° = 264°
- 2Arc length AC = (264/360) × 2 × π × 8.5 = (264/360) × 17π ≈ 39.14
- 3Two radii OA and OC add 8.5 + 8.5 = 17 cm
- 4Perimeter of sector AOC = arc length AC + 2 × radius = 39.14 + 17 = 56.14
- 5Rounded to 3 significant figures: 56.2
Answer56.2
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