ECZ 2022 · O-Level Paper 1 — Circle Theorems
In the following diagram, AB and AC are tangents to the circle, centre O. AC and BE produced, meet at D and angle BAC = 54°. Calculate angle (c) CDB.
- A. 54°
- B. 63°
- C. 36°
- D. 27°
Verified working — step 1
AB and AC are tangents from A, so AB = AC and triangle ABC is isosceles, giving angle ABC = angle ACB = 180° − 54°2= 63°. The line BD is BE produced and passes through the centre O, so it is a diameter line; a tangent is perpendicular to a diameter at the point of contact, hence angle ABD = 90°. Since A, C and D are collinear, angle BAD = angle BAC = 54°. In triangle ABD, angle CDB = angle ADB = 180° − 90° − 54° = …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