The radical axis of two circles having centres at `C_(1)` and `C_(2)` and radii `r_(1)` and `r_(2)` is neither intersecting nor touching any of the circles, if

Options

A. `C_(1)C_(2)=0`
B. `0 lt C_(1)C_(2)lt|r_(1)-r_(2)|`
C. `C_(1)C_(2)=|r_(1)-r_(2)|`
D. `|r_(1)-r_(2)| lt C_(1)C_(2) lt r_(1)+r_(2)`

Answer

B

Explanation

The radical axis of two circles will neither intersect nor touch any of the given circles in the following cases:
(i) When `C_(1)C_(2) lt r_(1)+r_(2)` (ii) When `0 lt C_(1)C_(2)lt|r_(1)-r_(2)|`
Hence, option (b) is correct.