Question:
The minimum distance between any two points $P_{1}$ and $P_{2}$ while considering point $P_{1}$ on one circle and point $\mathrm{P}_{2}$ on the other circle for the given circles' equations
$x^{2}+y^{2}-10 x-10 y+41=0$
$x^{2}+y^{2}-24 x-10 y+160=0$ is
Solution:
Given $\mathrm{C}_{1}(5,5), \mathrm{r}_{1}=3$ and $\mathrm{C}_{2}(12,5), \mathrm{r}_{2}=3$
Now, $C_{1} C_{2}>r_{1}+r_{2}$
Thus, $\left(P_{1} P_{2}\right)_{\min }=7-6=1$
