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PMN and PQR are two secants of the circle MQTRN and PT is a tangent....

Mathematics
JAMB 1991

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 centimeters
  • A. 7.3, 5.9
  • B. 7.7, 12.5
  • C. 12.5, 7.7
  • D. 5.9, 7.3
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Correct Answer: Option C
Explanation
\(\frac{PQ}{PN} = \frac{PM}{PR} = \frac{QM}{NR}\)

\(\frac{4.8}{12} = \frac{5}{PR}\)

PR = \(\frac{5 \times 12}{4.8} = \frac{50}{4}\)

= 12.5

\(\frac{PQ}{PN} = \frac{PM}{PT} = \frac{TM}{NT}\)

\(\frac{PT}{12} = \frac{5}{PR}\)

PT2 = 60

PT = \(\sqrt{60}\)

= 7.746

= 7.7

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