Circles on the Rim, 1
Sequence 1: Take each of the blue circles in turn as the starting point of an Arbelos chain.
Let be the outer circle, be the kth blue circle, and let them be tangent at .
To form the new (purplse) sequence, I need
1. The two radii
2. The line (vector) passing through the two centers
3. A point of tangency with another circle, , which is tangent to both .
The point satisfies 3. for every blue circle.