Question : 
In the figure, PT is a tangent. If TP = 12 cm, PB = $x$ + 7 cm, and PA = $x$ cm, then find the value of $x$.
Option 1: 9
Option 2: 6
Option 3: 7
Option 4: 5
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Correct Answer: 9
Solution :
TP = 12 cm
PB = $x$ + 7 cm
PA = $x$ cm
TP$^{2}$ = PA $\times$ PB
⇒ $12^{2} = x \times (x + 7)$
⇒ $144 = x^{2} + 7x$
⇒ $ x^{2} + 7x-144=0$
⇒ $(x-9)(x+16) = 0$
⇒ $x = 9$ or $x = -16$
But $x$ cannot take a negative value so $x$ = 9 cm
Hence, the correct answer is 9.
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