Question : Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB.
Option 1: $3\sqrt{2}$ cm
Option 2: $4\sqrt{2}$ cm
Option 3: $6\sqrt{3}$ cm
Option 4: $6\sqrt{2}$ cm
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Correct Answer: $6\sqrt{2}$ cm
Solution :
$R{_{C{_1}}} = 6$ cm
$R{_{C{_2}}} = 3$ cm
To find the length of the common tangent.
Length of direct common tangent = $\sqrt{d^2 - (R{_{C{_1}}} - R{_{C{_2}}})^2}$
Where $d = R{_{C{_1}}} + R{_{C{_2}}} = 9$ cm
$\therefore$ Length of common tangent $ = \sqrt{9^2 - (6 - 3)^2}$
$= \sqrt{81-3^2} = \sqrt{81-9} = \sqrt{72} = 6\sqrt2$ cm
Hence, the correct answer is $6\sqrt2$ cm.
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