The Apollonius-Toën circles

The Apollonius-Toën case

Question 2.1

What if we collapse all of the three red circles to one point?

\includegraphics[scale=0.2]{Images/all8circles/all8circles-0.png}
Answer 2.2

In this case we find infinitely many tangent circles!

\includegraphics[scale=0.2]{Images/all8circles/all8circles-0.png}
Question 2.3

How did we pass from 8 to infinitely many?

As we will see next section, the answer lies in the presence of redundancies!