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JAMB Mathematics 1991 Question 35

Question 35

Circle Theorems

Use the figure below to answer questions 35 and 36. PMN and PQR are two secants of the circle MQTRN and PT is a tangent.
If PM = 5cm, PN = 12cm and PQ = 4.8cm, calculate the respective lengths of PR and PT in centimetres

Diagram for this question
  1. A.7.3, 5.9
  2. B.7.7, 12.5
  3. C.12.5, 7.7
  4. D.5.9, 7.3
Show the answer and explanation

Answer: C (12.5, 7.7)

Explanation

For secants from the same point, PM × PN = PQ × PR, so 60 = 4.8 × PR and PR = 12.5. For the tangent, PT2 = PM × PN = 60, so PT ≈ 7.7.