Subproblem: To inscribe a circle in the knife.

_____________________[br]Archimedes' Arbelos:[br][list][br][*][b] →1a. Inscribe a circle in the arc.[/b][br][*]1b. Tangent circles in the arc (Solution 1).[br][*]1c. Vector Reduction: [url]http://www.geogebratube.org/material/show/id/54557[/url][br][*]1d. Ellipse from one parameter, scale and rotation: [url]http://www.geogebratube.org/material/show/id/55256[/url][br][*]1e. Final Construction: [url]http://www.geogebratube.org/material/show/id/54592[/url][br][br][*]2a. Let one circle enclose another.[br] Inscribe a third circle in the ring: [url]http://www.geogebratube.org/material/show/id/54595[/url] [br][*]2b. Tangent circles in the ring. [url]http://www.geogebratube.org/material/show/id/54596[/url] [br][/list][br]3. Cyclic Solution:[br][list][br][*]3a. An outer ring of tangent circles: [url]http://www.geogebratube.org/material/show/id/55009[/url] [br][*]3b. Determine the projection.[br][*]3c. Final Construction: [url]http://www.geogebratube.org/material/show/id/55883[/url][br][/list]