ECZ 2017 · O-Level Paper 1 — Circle Theorems

In the diagram, A, B, C, D, E and F lie on the circumference of a circle, with angle FBD = 70° and angle AEF = 20°. Explain why AD is a diameter.

A. Because AD passes through the centre by inspection
B. Because AD is the longest chord in the diagram
C. Because angle AFD = 70° − 20° = 50°, doubling to 100°
D. Because angle ACD = angle ACF + angle FCD = 20° + 70° = 90°, and a 90° inscribed angle stands on a diameter

Verified working — step 1

Angle ACF = 20° (same segment as angle AEF, on arc AF) and angle FCD = 70° (same segment as angle FBD, on arc FD). So angle ACD = 20° + 70° = …

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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