Two unequal circles can be projected to equal ones. I use the same projection as in the Arbelos problem ([url]http://www.geogebratube.org/material/show/id/54557[/url] ). The bounding circle of the figure has become a line. A good way to solve a general problem is to start with a particular case. Here, I begin with the [i]initial position[/i]: the circle tangent to [math]\;\;[/math] - two tangent circles of equal radii [math]\;\;[/math]-a straight line tangent to both.
Now to tackle the chain! _________________ The Tangent Circle Problem: [list] [*]1. Tangent along the rim: solve for k [*][b]→2a. Initial position:[/b] [*]2b. Tangent chain to equal circles [url]http://www.geogebratube.org/material/show/id/58455[/url] [*]3a. Four mutually tangent & exterior circles (Apollonius): [url]http://www.geogebratube.org/material/show/id/58189 [/url] [*]3b. Vector reduction: [url]http://www.geogebratube.org/material/show/id/58461[/url] [/list] [list] [*]Affine Transformation [url]http://www.geogebratube.org/material/show/id/58177[/url] [*]Reflection: Line about a Circle [url]http://www.geogebratube.org/material/show/id/58522[/url] [*]Reflection: Circle about a Circle: [url]http://www.geogebratube.org/material/show/id/58185[/url] [*]Circle Inversion: Metric Space: [url]http://www.geogebratube.org/material/show/id/60132[/url] [/list] Solution: [list] [*]Sequences 1: Formation [url]http://www.geogebratube.org/material/show/id/58896[/url] [*]Sequence 1: Formation [url]http://www.geogebratube.org/material/show/id/59816[/url] [*]Sequence 1: Iteration 1 [url]http://www.geogebratube.org/material/show/id/59828[/url] [*]Example of equivalent projections: [url]http://www.geogebratube.org/material/show/id/65754[/url] [*]Final Diagram: [url]http://www.geogebratube.org/material/show/id/65755[/url] [/list]