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  4. 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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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:

Conic Sections

Solution:

as we know $L_{\text {int }}=\sqrt{d^2-\left(r_1+r_2\right)^2}=7$
$L_{e x t}=\sqrt{d^2-\left(r_1-r_2\right)^2}=11$
squaring & subtact $r_1 r_2=18$