4MA1/1HR Jan 2022, 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
Points A, B, C, D lie on a circle with centre O, and AOC is a diameter with angle BAC = 55°. Find angle ADB, justifying each step.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Angle ABC = 90° because it is the angle in a semicircle
- 2In triangle ABC, angles add up to 180°, so angle ACB = 180° − 90° − 55° = 35°
- 3Angle ADB = angle ACB because they are angles in the same segment
- 4So angle ADB = 35°
Answer35
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