S₁ : The condition that the line  $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ to be a tangent of the circle ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{r}}^2$ is $C^2=r^2\left(1+m^2\right)$ .       
S₂ : The condition that the line $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ to be a tangent of a circle is r= d. Where r is the radius of the circle and d is the distance from the centre of the circle to the line