The two circles $x^{2} + y^{2} = c^{2} (c > 0)$ touch each other if:

2 | a | = C

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| a | = C

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a = 2 c

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| a | = 2 c

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Solution

The correct option is B $2 | a | = C$
We have,

As centre of one circle is $(0, 0)$ and other circle passes through the $(0, 0)$ .

Therefore,

Also $C_{1} (\frac{a}{2}, 0)$ and $C_{2} (0, 0)$ .

Then,

$r_{1} = \frac{a}{2} r_{2} = c$

$\Rightarrow C_{1} C_{2} = r_{1} - r_{2} = \frac{a}{2}$

$\Rightarrow C = \frac{a}{2} = \frac{a}{2}$

$C = a$
If two circles touches each other they must be touch each other internally.

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