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# The two circles $x^2+y^2=ax$ and $x^2+y^2=c^2\; (c > 0)$ touch each other if

$\begin{array}{1 1}(A)\;|a|=c \\(B)\;a=2c \\(C)\;|a|=2c \\(D)\;2|a|=c \end{array}$

As centre of one circle is $(0,0)$ and other circle passes through $(0,0)$ therefore Also $C_1(\frac{a}{2},0),C_2 (0,0)$
$r_1=\large\frac{a}{2}$$r_2=c$
$C_1C_2=r_1-r_2=\large\frac{a}{2}$
$C-\large\frac{a}{2}=\frac{a}{2}$
$C=a$
If the two circles touch each other then they must touch each other internally.
Hence A is the correct answer.