From a point P outside a circle, a tangent PA and a secant PBC are drawn. If PA = 6 cm and BC = 5 cm; what is the length of the segment PB?
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 4 cm.
Let PB = x cm
PC = PB + BC = (x + 5) cm
PA2 = PB × PC
⇒ 62 = x(x + 5)
⇒ 36 = x(x + 5)
⇒ x2 + 5x – 36 = 0
⇒ (x + 9)(x – 4) = 0
⇒ x - 4 = 0
⇒ x = 4 cm