I found it easier to work through the Arbelos problem by using an ellipse with a major half-axis of 1 (bound in the unit circle). This ellipse has only one parameter. Then the whole problem can be scaled and rotated.
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Archimedes' Arbelos:
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[*]1a. Inscribe a circle in the arc.[url]http://www.geogebratube.org/material/show/id/54105[/url]
[*]1b. Tangent circles in the arc (Solution 1).
[*]1c. Vector Reduction: [url]http://www.geogebratube.org/material/show/id/54557[/url]
[*][b]→1d. Proposition: To give an ellipse by one parameter, scale and rotation.[/b]
[*]1e. Final Construction: [url]http://www.geogebratube.org/material/show/id/54592[/url]
[*]2a. Let one circle enclose another.
Inscribe a third circle in the ring: [url]http://www.geogebratube.org/material/show/id/54595[/url]
[*]2b. Tangent circles in the ring. [url]http://www.geogebratube.org/material/show/id/54596[/url]
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3. Cyclic Solution:
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[*]3a. An outer ring of tangent circles: [url]http://www.geogebratube.org/material/show/id/55009[/url]
[*]3b. Determine the projection.
[*]3c. Final Construction: [url]http://www.geogebratube.org/material/show/id/55883[/url]
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