ECZ 2021 · GCE Paper 1 — Circle Theorems
In the diagram, A, B, C and D are points on the circumference of a circle, centre O, with angle DAB = 36°, BC = CD and EBF a tangent to the circle at B. Find angle CBF.
- A. 144°
- B. 72°
- C. 36°
- D. 18°
Verified working — step 1
Triangle BCD has CB = CD and angle BCD = 144°, so the two base angles are (180° − 144°) ÷ 2 = 18° each; in particular angle BDC = 18°. By the alternate segment theorem, the angle between tangent BF and chord BC equals the angle BDC in the alternate segment, so angle CBF = …The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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