4MA1/2H Jan 2020, Question 13: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
Points A, B, C, D lie on a circle with centre O, AOD a diameter, angle CBD = 28° and angle BDA = 32°. Find angle BDC, justifying each step.
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Solution · 4 marks
- 1Angle CBD = 28°, so angle CAD = 28° (angles in the same segment are equal)
- 2Angle ABD = 90° (angle in a semicircle is 90°)
- 3In triangle ABD, angle BAD = 180° − 90° − 32° = 58°
- 4Angle BAC = angle BAD − angle CAD = 58° − 28° = 30°
- 5Angle BDC = angle BAC (angles in the same segment are equal)
- 630
Answer30
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