ECZ 2015 · O-Level Paper 2 · Question 3 — Circle Theorems
Question from ECZ 2015 · O-Level Paper 2 · Question 3
(a) In the diagram below, a circle with centre O passes through the points Q, U, S and V. TP and TR are tangents to the circle at the points Q and S respectively. Angle VQO = 20° and angle QVS = 60°. Find
(a(i)) angle QUS,[1]
Verified working — step 1
VQUS is a cyclic quadrilateral.(a(ii)) angle VQP,[1]
Verified working — step 1
A tangent meets the radius at 90°, so angle OQP = 90°.(a(iii)) angle PTR,[2]
Verified working — step 1
Angle at the centre is twice the angle at the circumference: angle QOS = 2 × 60 = 120°.(a(iv)) reflex angle SOQ,[1]
Verified working — step 1
The minor angle SOQ is 120°.(a(v)) the length ST, given that OS = 3 cm and OT = 15 cm.[2]
Verified working — step 1
The tangent at S is perpendicular to the radius OS, so triangle OST is right-angled at S.(b) Express 4x - 2 - 2x + 3 as a single fraction in its simplest form.[3]
Verified working — step 1
Common denominator (x - 2)(x + 3).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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