Proof of the Arbelos Theorem - 2

I have written a computational proof of the arbelos theorem and uploaded it to the "Articles" page of my website, MathCelebration. Here are the exact URLs of the two files (though clicking on them will open the documents in Google Docs):

• Arbelos proof - screen version
• Arbelos proof - print version

If you glance through the proof, you will see that it is highly computational, but it uses nothing more advanced or complicated than the theorem of Pythagoras.

The link I gave earlier takes you to the original "pure geometry" proof given by Archimedes, but it shows the congruence only of $\omega_4$ and $\omega_5$. The above proof establishes that $\omega_7$ too has the same radius.

I close with a rather challenging question:

Given the configuration with circles $\omega_1$, $\omega_2$ and $\omega_3$, how will you geometrically construct circles $\omega_4$, $\omega_5$, $\omega_6$ and $\omega_7$? 

(Here, "geometrically" means that we work only with Euclidean instruments.)