Question : In the given figure, PAB is a secant and PT is a tangent to the circle from P. If PT = 8 cm, PA = 6 cm, and AB = $x$ cm, then the value of $x$ is:
Option 1: $\frac{14}{9}$
Option 2: $\frac{1}{3}$
Option 3: $\frac{14}{3}$
Option 4: $\frac{4}{3}$
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Correct Answer: $\frac{14}{3}$
Solution :
As we know,
PT
2
= PA × PB
⇒ 8
2
= 6($x$ + 6)
⇒ 64 = 6$x$ + 36
⇒ $x$ = $\frac{28}{6} = \frac{14}{3}$
Hence, the correct answer is $\frac{14}{3}$.
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