ECZ 2014 · O-Level Paper 2 · Question 3 — Circle Theorems
Question from ECZ 2014 · O-Level Paper 2 · Question 3
(a) In the diagram below, P, Q, R and S are points on the circumference of a circle with centre O. AQB is a tangent to the circle at Q. Given that PS = PQ, QR = RS and angle PSQ = 70°, calculate
(a(i)) angle QPS,[1]
Verified working — step 1
PQ = PS, so triangle PQS is isosceles and the base angles are equal.(a(ii)) angle QRS,[1]
Verified working — step 1
PQRS is a cyclic quadrilateral.(a(iii)) angle AQP,[1]
Verified working — step 1
AQ is a tangent and QP a chord.(a(iv)) angle SOQ.[1]
Verified working — step 1
Angles SOQ and QPS both stand on arc SQ.(b) Solve the equation 1 - 2m - 5m2 = 0, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
Rearrange to standard form: 5m2 + 2m - 1 = 0, so a = 5, b = 2, c = -1.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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