Seminar: Week 2

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.