Two circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$ touch each other externally and both touch a line $l$. A circle $C_3$ with radius $r_3 < r_1, r_2$ is tangent to $l$ and externally to $C_1$ and $C_2$. Prove that \[\frac{1}{\sqrt{r_3}}=\frac{1}{\sqrt{r_2}}+\frac{1}{\sqrt{r_2}}.\]