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.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 9.
PT2 = PA × PB
⇒ 144 = x(x + 7)
⇒ 144 = x2 + 7x
⇒ x2 + 7x - 144 = 0
⇒ x2 + 16x - 9x - 144 = 0
⇒ x(x + 16) - 9(x + 16) = 0
⇒ (x - 9)(x + 16) = 0
⇒ x = 9; x = -16 (cannot be negative)
⇒ x = 9 cm