Question : Two circles touch each other externally, having a radius of 12 cm and 8 cm, respectively. Find the length of their common tangent AB with point A on the bigger circle and B on the smaller circle.
Option 1: $8 \sqrt{6} \mathrm{~cm}$
Option 2: $8 \sqrt{3} \mathrm{~cm}$
Option 3: $12 \sqrt{3} \mathrm{~cm}$
Option 4: $12 \sqrt{6} \mathrm{~cm}$
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Correct Answer: $8 \sqrt{6} \mathrm{~cm}$
Solution :
Given: $R_1$ = 12 cm
$R_2$ = 8 cm
Thus, direct common tangent = $2\sqrt{R_1R_2}$
= $2\sqrt{12×8}$
= $8\sqrt{6}$
Hence, the correct answer is $8 \sqrt{6} \mathrm{~cm}$.
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