Question : Two circles touch each other externally. The radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.
Option 1: $6 \sqrt{6} \mathrm{~cm}$
Option 2: $8 \sqrt{3} \mathrm{~cm}$
Option 3: $8 \sqrt{2} \mathrm{~cm}$
Option 4: $8 \sqrt{6} \mathrm{~cm}$
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Correct Answer: $8 \sqrt{6} \mathrm{~cm}$
Solution :
Given:
$r{_1}=12, r{_2}=8$
Length of the direct common tangent
$=\sqrt{d^2-(r{_1} -r{_2})^2}$ where $d=r{_1}+r{_2}$
$=\sqrt{(12+8)^2-(12-8)^2}$
$=\sqrt{20^2 - 4^2} = \sqrt{400-16}=\sqrt{384}=8\sqrt6$ cm
Hence, the correct answer is $8 \sqrt{6} \mathrm{~cm}$.
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