ECZ 2019 · GCE Paper 1 — Circle Theorems
In the diagram, A, B, C, D and E are points on the circumference of a circle with centre O. DE = AD, AĈB = 20° and AÔE = 80°. Find BÂD.
- A. 50°
- B. 70°
- C. 90°
- D. 30°
Verified working — step 1
Work with arcs. AĈB = 20° puts arc AB at 40°; AÔE = 80° puts arc AE at 80°. Equal chords DE and AD give equal arcs, and the remaining arcs must total 360°, which forces arc ED = arc DA(through the far side) = 140° each... solving, the arc from B to D (through C) is 100°, so the inscribed angle BÂD = 100° ÷ 2 = …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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