ECZ 2017 · O-Level Paper 1 — Circle Theorems

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

"Explain why" needs a THEOREM, not an eyeball: prove the angle on AD is 90°, and the diameter follows.

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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