Question : In a circle centred at O, PQ is a tangent at P. Furthermore, AB is the chord of the circle and is extended to Q. If PQ = 12 cm and QB = 8 cm, then the length of AB is equal to:
Option 1: 20 cm
Option 2: 4 cm
Option 3: 10 cm
Option 4: 8 cm
Correct Answer: 10 cm
Solution :
Given: PQ = 12 cm
BQ = 8 cm
Let the length of the chord be $x$.
We know that,
$PQ^2 = AQ \times BQ$
⇒ $12^2 = (x + 8) \times 8$
⇒ $\frac{144}{8} = x + 8$
⇒ $18 = x + 8$
⇒ $x = 18 - 8$
⇒ $x = 10$
Hence, the correct answer is 10 cm.
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