Let a circle $C:(x-h{)}^2+(y-k{)}^2=r^2,k>0$, touch the x-axis at (1,0). If the line $x+y=0$ intersects the circle C at P and Q such that the length of the chord PQ  is 2 , then the value of h+k+r is equal to

Circle touches xaxis at (1,0)

$$\begin{gathered} \Rightarrow radius = r=k \\ \Rightarrow perpendicular dis\tan ce from (1,r) tothe line x+y=0 is\left|\frac{r+1}{\sqrt{2}}\right| \end{gathered}$$

 $$\begin{gathered} \Rightarrow \mathrm{OR}=\left|\frac{\mathrm{r}+1}{\sqrt{2}}\right| \\ \begin{array}{r}\Rightarrow r^2=1+\frac{(r+1{)}^2}{2}\\ 2r^2=2+r^2+1+2r\\ r^2-2r-3=0\\ (r-3)(r+1)=0\\ r=3,-1\end{array} \end{gathered}$$

The value of h+k+r is equal to 1+3+3=7.