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Q.

If the length of a common internal tangent to two circles is 7 , and that of a common external tangent is 11, then the product of the radii of the two circles is

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answer is 18.

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Detailed Solution

Question Image

From the above figure,

$\begin{aligned} L_{in} = \sqrt{d^{2} - {(r_{1} + r_{2})}^{2}} = 7 \\ and & L_{ex} = \sqrt{d^{2} - {(r_{1} - r_{2})}^{2}} = 11 \end{aligned}$

Squaring and subtracting, we get $r_{1} r_{2} = 18$

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