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The length of common internal tangent to...

The length of 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

Text Solution

Verified by Experts

The correct Answer is:
18

From the above figure
`L_("in")=sqrt(d^(2)-(r_(1)+r_(2))^(2))=7`
and `L_("ex")=sqrt(d^(2)-(r_(1)-r_(2))^(2))=11`
Squaring and subtracting, we get `r_(1)r_(2)=18`.
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