4024/12 Oct/Nov 2025, Question 14: Combining Circle Theorems
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Find angle BCD using circle centre O, tangent EF at A, angle BAF = 65° and angle AOD = 80°, justifying each step with a geometrical property.
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Solution · 4 marks
- 1Angle BCA = angle BAF = 65° (alternate segment theorem)
- 2Angle ACD = 80 ÷ 2 = 40° (angle at the centre is twice the angle at the circumference)
- 3Angle BCD = 65 + 40 = 105°
Answer105° angle BCA = 65°, alternate segment theorem angle ACD = 40°, angle at the centre is twice the angle at the circumference
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