ECZ 2012 · O-Level Paper 1 — Similarity and Congruency
The diagram shows two circles with the same centre O. The radius of the smaller circle is 5 cm and that of the larger is 15 cm. Chord AB is 7 cm and angle ABO = angle DCO = 40 degrees. Calculate the length of the chord CD.
- A. 14 cm
- B. 21 cm
- C. 23 cm
- D. 7 cm
Verified working — step 1
Triangle OAB is isosceles with OA = OB = 5 and base angles 40 degrees; triangle ODC is isosceles with OD = OC = 15 and the same base angles. Equal base angles make the triangles similar, with side ratio 155= 3. So CD = 3 x 7 = …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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