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
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