Question : A and B are centres of two circles of radii 11 cm and 6 cm, respectively. PQ is a direct common tangent to the circles. If AB = 13 cm, then the length of PQ will be:
Option 1: 8.5 cm
Option 2: 13 cm
Option 3: 12 cm
Option 4: 17 cm
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Correct Answer: 12 cm
Solution :
Length of direct common tangent $PQ = \sqrt{AB^2-(r_1-r_2)^2}$
$= \sqrt{13^2-(11-6)^2}$
$= \sqrt{13^2-5^2}$
$= \sqrt{169-25}$
$= \sqrt{144}$
$=12$ cm
Hence, the correct answer is 12 cm.
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