Three circles $O_1(r_1)$, $O_2(r_2)$ and $O_3(r_3)$ touch each other externally. The line $l$ is tangent to $O_1(r_1)$ and parallel to the exterior common tangent $m$ to $O_2(r_2)$ and $O_3(r_3)$ which does not intersect $O_1(r_1)$. Find the distance between the lines $l$ and $m$.
I tried using Pythagoras theorem and got the following equations $$(h+r_3-r_2)^2 + (2\sqrt{r_2r_3}-x)^2 = (r_1 +r_2) ^2$$ $$h^2+x^2=(r_1+r_3)^2$$ where $r_1 + r_3 + h$ is the required length. I don't know how to proceed i.e. how to isolate $h$ in terms of $r_1$,$r_2$ and $r_3$.