Which of the following equations can represent a triangle:

         $\left|z-1\right|=\left|z-2\right|=\left|z-i\right|$ 

(i)      $\left|z-1\right|=\left|z-i\right|$

Represents a straight line through origin i.e., $y=x$

(ii)         $\left|z-1\right|=\left|z-2\right|\Rightarrow x=\frac{3}{2}$

which is a straight line

(iii)        $\left|z-2\right|=\left|z-i\right|\Rightarrow 4x-2y=3$

which  is a straight line