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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