The total number of circles that can be drawn touching all the three lines $\mathrm{x}+\mathrm{y}-1=0, \mathrm{x}-\mathrm{y}-1=0, \mathrm{y}+1=0$ is

$\left|\begin{array}{ccc}1& 1& -1\\ 1& -1& -1\\ 0& 1& 1\end{array}\right|\ne 0$

Give liens are not concurrent and no two are are parallel.

The given lines forms a triangle. Therefore number of circles touching  given lines =4