4MA1/1HR Jan 2020, Question 14: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
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The question, in short
Circle with centre O and points A, B, C on it; angle ABC = 38°. Find angle OAC, justifying each stage of the working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 138 × 2 = 76
- 2Angle at the centre is twice the angle at the circumference
- 3Triangle AOC has angles at A and C equal because OA = OC (radii)
- 4So base angles in isosceles triangle AOC are equal
- 5(180 − 76) ÷ 2 = 52
- 6Angle OAC = 52
Answer52
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