Mutually Exterior & Tangent Circles, 2
- Author:
- Ryan Hirst
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...)
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The Tangent Circle Problem:
- 1. Tangent along the rim: solve for k
- 2a. Initial position: http://www.geogebratube.org/material/show/id/58360
- 2b. Tangent to equal circles: http://www.geogebratube.org/material/show/id/58455
- 3a. Four mutually tangent & exterior circles (Apollonius): http://www.geogebratube.org/material/show/id/58189
- →3b. Vector reduction
- Affine Transformation http://www.geogebratube.org/material/show/id/58177
- Reflection: Line about a Circle http://www.geogebratube.org/material/show/id/58522
- Reflection: Circle about a Circle: http://www.geogebratube.org/material/show/id/58185
- Circle Inversion: Metric Space: http://www.geogebratube.org/material/show/id/60132
- Sequences 1: Formation http://www.geogebratube.org/material/show/id/58896
- Sequence 1: Formation http://www.geogebratube.org/material/show/id/59816
- Sequence 1: Iteration 1 http://www.geogebratube.org/material/show/id/59828
- Example of equivalent projections: http://www.geogebratube.org/material/show/id/65754
- Final Diagram: http://www.geogebratube.org/material/show/id/65755