The definitions have been rewritten as linear combinations of the given positions of A,B. Scalar parameters: radii a, b, and rotation angle to C.
I think it can be aggressively simplified by taking advantage of half-angle formulas, along with the observation that the theorem 'inscribed angles which are subtended by equal arcs are equal' holds at the point of tangency. But I think a better a approach is to go back to projection. (Try opening the worksheet and writing down the full vector algebra which gives point D. I have taken a Very Bad way to solve a not-too-complicated tangency case. Let me find a better one...) _________________ The Tangent Circle Problem: [list] [*]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] [*][b]→3b. Vector reduction[/b] [/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]