A rain of implications (Unbearable lightness of the derivations...)
1. Conjugated disks : $D + D' =2(A+B+C)$.
2. (Generalized) Pappus' chains: $C_{n+1}= 2C_n - C_{n-1} + 2(A+B)$.
3. Pappus thread: $K=\pm \frac{A-B}{2}$.
4. Mid-circle: $T= \pm \frac{A+B+C-D}{2}$.
5. Points of tangency: $P=\frac{A+B}{2}$.
6. Apollonian group.
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