ECZ 2016 · GCE Paper 2 · Question 3 — Circle Theorems
ABDG is a circle with centre O; GBD = 21°, BC and CE are tangents at B and D.
(a(i)) Calculate GOD.[1]
Verified working — step 1
Angle GOD and angle GBD stand on the same arc GD, with GOD at the centre and GBD at the circumference.(a(ii)) Calculate GFE.[1]
Verified working — step 1
Since BG is a diameter, angle BDG = 90° (angle in a semicircle).(a(iii)) Calculate GED.[1]
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Since AD is a diameter, angle AGD = 90° (angle in a semicircle).(a(iv)) Calculate BCD.[2]
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OB ⊥ CB and OD ⊥ CD (radius ⊥ tangent), so angle OBC = angle ODC = 90°.(b) Solve the equation x2 + 2x = 5, giving your answers correct to 2 decimal places.[5]
Verified working — step 1
x2 + 2x = 5 → x2 + 2x − 5 = 0The 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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