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:

qImage660a21425b88bbe1b8a27b97

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 1)
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  1. \(\frac{14}{9}\)
  2. \(\frac{1}{3}\)
  3. \(\frac{14}{3}\)
  4. \(\frac{4}{3}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{14}{3}\)
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Detailed Solution

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Given:

PT = 8 cm

PA = 6 cm

Formula used

PT2 = PA × PB

Here, PT is tangent

Calculation:

qImage660a21425b88bbe1b8a27b97

Let AB be "x"

PT2 = PA × PB

82 = 6(6 + x)

32/3 = 6 + x

x = 14/3

The value of AB is 14/3 cm.

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