ECZ 2016 · GCE Paper 2 · Question 3 — Circle Theorems
Question from ECZ 2016 · GCE Paper 2 · Question 3
(a) In the diagram below, ABDG is a circle with centre O. Given that angle GBD = 21°, BC and CE are tangents to the circle at B and D respectively, calculate
(a(i)) angle GOD,[1]
Verified working — step 1
Angles GOD and GBD both stand on the same arc GD.(a(ii)) angle GFE,[1]
Verified working — step 1
BG is a diameter, so angle BDG = 90° (angle in a semicircle).(a(iii)) angle GED,[1]
Verified working — step 1
AD is a diameter, so angle AGD = 90° (angle in a semicircle).(a(iv)) angle BCD.[2]
Verified working — step 1
A radius meets a tangent at 90°, 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
Rearrange to standard form: x2 + 2x - 5 = 0, so a = 1, b = 2, c = -5.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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question