The number of common tangents to the circles ${\text{x}}^2+{\mathrm{y}}^2-10\mathrm{x}-10\mathrm{y}+41=0$ and ${\mathrm{x}}^2+{\mathrm{y}}^2-16\mathrm{x}-10\mathrm{y}+80=0$ is :

$\begin{array}{l}{\mathrm{C}}_1(5,5),{\mathrm{C}}_2(8,5)\\ {\mathrm{r}}_1=\sqrt{25+25-41}=3,{\mathrm{r}}_2=\sqrt{64+25-80}=3\\ {\mathrm{C}}_1{\mathrm{C}}_2=\sqrt{3^2+0}=3\\ \left|{\mathrm{r}}_1-{\mathrm{r}}_2\right|<{\mathrm{C}}_1{\mathrm{C}}_2<{\mathrm{r}}_1+{\mathrm{r}}_2\end{array}$
Intersecting circles 
No.of common tangents = 2.