ECZ 2012 · O-Level Paper 2 · Question 3 — Circle Theorems
Question from ECZ 2012 · O-Level Paper 2 · Question 3
(a) In the diagram below, A, B, C and D are points on the circumference of a circle. TCM and MDE are tangents to the circle at C and D respectively. Given that AB = AD, angle CBD = 47° and angle BDC = 23°, calculate
(a(i)) angle BCT,[1]
Verified working — step 1
TC is a tangent and CB a chord.(a(ii)) angle BAD,[1]
Verified working — step 1
In triangle BCD: angle BCD = 180 - 47 - 23 = 110°.(a(iii)) angle ABD,[1]
Verified working — step 1
AB = AD, so triangle ABD is isosceles with base BD.(a(iv)) angle DMC.[2]
Verified working — step 1
By the alternate segment theorem, angle MCD = angle CBD = 47 and angle MDC = angle CAD = 47.(b) Solve the equation 2x2 + 5x - 8 = 0, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
a = 2, b = 5, c = -8.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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