4MA1/2HR Jun 2020, Question 19: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Circle centre O radius 12 cm, points A, B, C, D on it; sector OADC area 100 cm². Find angle ABC to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Sector area: (angle AOC ÷ 360) × π × 12² = 100
- 2Angle AOC = 100 × 360 ÷ (144π) = 79.58°
- 3Angle at the centre is twice the angle at the circumference.
- 4Angle ABC = 79.58 ÷ 2 = 39.8
Answer39.8
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