4MA1/1HR Jun 2024, Question 13: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Points A, B, C, D lie on a circle with centre O; angle BCD = 128°. Find angle OBD, justifying each stage of the working.
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Solution · 5 marks
- 1Angle BAD = 180° − 128° = 52° (opposite angles of a cyclic quadrilateral add to 180°)
- 2Angle BOD = 2 × 52° = 104° (angle at the centre is twice the angle at the circumference)
- 3OB = OD because both are radii, so triangle OBD is isosceles
- 4Angle OBD = (180° − 104°) ÷ 2 = 38 (angles in a triangle add to 180°)
Answer38
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