Steiner chain of circles
Given two circles C1
, and C2
In the area between these two circles, we draw a circle K1
touching both C1 and C2,
then a circle K2
touching both C1, C2 and K1,
touching C1, C2 and K2 ...
Kn touching C1, C2 and Kn-1.
Locus of centers of circles K Solution
Sometimes, this chain closes and Kn also touches K1 !
Prove that in this case, we can choose the first circle anywhere, and the chain may then "rotate" freely
Deduce a criterion for such a chain to exist.