The minimum distance between any two points $P_1$ and $P_2$ while considering point $P_1$ on the circle and point $P_2$ on the other circle for the given circles’ equations

$$\begin{gathered} x^2+y^2-10x-10y+41=0, \\ {x}^2+y^2-24x-10y+160=0 is \end{gathered}$$

For circle, $x^2+y^2-10x-10y+41=0$
Centre $C_1\equiv (5,5)$ and radius, $r_1=3$
For circle, $x^2+y^2-24x-10y+160=0$
Centre $C_2\equiv (12,5)$ and radius, $r_2=3$
$C_1{C}_2=7>r_1+r_2\Rightarrow$ Circles are separated
$\therefore$ Required minimum possible distance, $P_1{P}_2=7-(3+3)=1$