4MA1/2HR Jun 2018, Question 12: Tangent Properties of a Circle
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks
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The question, in short
A circle with centre O passes through A, C and D; tangents from B touch at A and C, with angle ABC = 74°. Calculate angle ADC, showing each step of reasoning.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1Angle OAB = 90° (tangent-radius property)
- 2Angle OCB = 90° (tangent-radius property)
- 3Angle ABC = 74°
- 4Angle COA = 360° − (90° + 90° + 74°) = 106°
- 5Angle ADC = 106° ÷ 2 = 53°
Answer53
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