4MA1/2HR Jun 2019, Question 15: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Points A, B, C, D lie on a circle centre O, with AOC a diameter and angle AOD = 98°. Find angle DBC, justifying each step.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 198° ÷ 2 = 49°
- 2Angle ABD = 49° (angle at the circumference is half the angle at the centre, standing on arc AD)
- 3Angle ABC = 90° (angle in a semicircle, since AOC is a diameter)
- 4Angle DBC = 90° − 49° = 41°
Answer41°
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