ECZ 2018 · GCE Paper 1 — Circle Theorems
In the diagram, RWS is a tangent to the circle at W. The points V, W, X and Y are on the circle such that XŶW = 44°, VŴY = 54° and SŴV = 39°. Calculate YX̂W.
- A. 88°
- B. 93°
- C. 98°
- D. 83°
Verified working — step 1
Split YX̂W into YX̂V + VX̂W. YX̂V stands on chord YV, as does VŴY, so YX̂V = 54°. By the alternate segment theorem on chord WV, VX̂W = SŴV = 39°. So YX̂W = 54° + 39° = 93°. (Check: triangle WXY then has 44° + 93° + 43° = …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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