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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