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

- a = 2c
- |a| = 2c
- |a| = c
- 2|a| = c

**Answer**

x^{2} + y^{2} = ax

Centre c_{1}(-a/2,0) and radius r_{1} = |a/2|

x^{2} + y^{2} = c^{2}

Centre c_{2}(0,0) and radius r_{2} = c

Both touch each other iff

|c_{1} + c_{2}| = r_{1} ± r_{2}

a^{2}/4 = (±a/2±c)^{2}

a^{2}/4 = a^{2}/4 ± |a|c + c^{2}

**The correct option is C.**