The two circles x2 + y2 = ax, and x2 + y2 = c2 (c > 0) touch each other if :
Solutions · 1
Official solution
As center of one circle is \[\left( {0,0} \right)\] and other circle passes through (0,0), therefore
Also \[{C_1}\left( {{a \over 2},0} \right){C_2}\left( {0,0} \right)\]
\[{r_1} = {a \over 2}{r_2} = C\]
\[{C_1}{C_2} = {r_1} - {r_2} = {a \over 2}\]
\[ \Rightarrow C - {a \over 2} = {a \over 2}\]
\[ \Rightarrow C = a\]
If the two circles touch each other, then they must touch each other internally.