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If the radii of two circles are 7 cm, 2 cm respectively and the distance between their centres is 13cm, then the length of their direct common tangent is

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20 cm

12 cm

9 cm

3 cm

answer is C.

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Detailed Solution

$d = 13, r_{1} = 7, r_{2} = 2$
Length of direct common tangent is
$\begin{array}{l} = \sqrt{d^{2} - {(r_{1} - r_{2})}^{2}} \\ = \sqrt{13^{2} - (7 - 2)^{2}} \\ = \sqrt{13^{2} - 5^{2}} \\ = 12 cm \end{array}$

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