Three circles are tangent to each other and also a common line, as shown. Let the radii of circles $O_1$, $O_2$, and $O_3$ be $r_1$, $r_2$, and $r_3$, respectively. Show that $$\frac{1}{\sqrt{r_3}}=\frac{1}{\sqrt{r_1}} +\frac{1}{\sqrt{r_2}}$$