Little theorem without proof: The reflection of a line about a circle, is a circle.
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The Tangent Circle Problem:
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[*]1. Tangent along the rim: solve for k
[*]2a. Initial position: [url]http://www.geogebratube.org/material/show/id/58360[/url]
[*]2b. Tangent 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]
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[*]Affine Transformation [url]http://www.geogebratube.org/material/show/id/58177[/url]
[*][b]→Reflection: Line about a Circle[/b]
[*]Reflection: Circle about a Circle [url]http://www.geogebratube.org/material/show/id/58185[/url]
[*]Circle Inversion: The Metric Space [url]http://www.geogebratube.org/material/show/id/60132[/url]
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Iteration:
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[*]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]
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