I have divided the problem into a number of subproblems.
First, the matter of inscribing a circle in the knife ark.
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Archimedes' Arbelos:
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[*][b] →1a. Inscribe a circle in the arc.[/b]
[*]1b. Tangent circles in the arc (Solution 1).
[*]1c. Vector Reduction: [url]http://www.geogebratube.org/material/show/id/54557[/url]
[*]1d. Ellipse from one parameter, scale and rotation: [url]http://www.geogebratube.org/material/show/id/55256[/url]
[*]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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