Question : Chord AB of a circle is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. PC = 12 cm, and BP = 10 cm, then the length of AB (in m) is:
Option 1: 5.4
Option 2: 6
Option 3: 5
Option 4: 4.4
Correct Answer: 4.4
Solution : PC=12 cm BP=10 cm PC 2 = AP × BP Let AB be $x$. AP = AB + PB = $x+10$ PC 2 = AP × BP $12^2 = (x+10) × 10 $ ⇒ $\frac{144}{10} = x + 10$ ⇒ $x+10 = 14.4$ ⇒ $x = 4.4$ Hence, the correct answer is 4.4.
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