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Two Circles Touching Internally and Externally

Based on the ...

Question

Based on the following.
Two circles of radius $r_{1}$ and $r_{2}$ are drawn. The distance between their centres is $d$ .
The condition that one is inside another and with no common point.

A

r_{1} + r_{2} = d

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B

r_{1} - r_{2} = d; r_{1} > r_{2}

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C

r_{1} + r_{2} > d

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D

r_{1} - r_{2} > d; r_{1} > r_{2}

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Solution

The correct option is B $r_{1} - r_{2} > d; r_{1} > r_{2}$
If radius of bigger circle is $r_{1}$ and radius of smaller circle is $r_{2}$ ,
then for smaller circle to lie completely inside, we must have
$r_{1} - r_{2} >$ distance between their centres $= d$

Hence option 'D' is correct choice

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