Arbelos Chain, Final

Let one circle enclose another. Proposition: [i]to construct a chain of tangent circles in the ring.[/i] General solution in a closed figure: bounding circle and image superimposed. n varies the radius of the enclosed circle. The limiting figure as n→∞, is the Shoemaker's knife. _____________________ Archimedes' Arbelos: [list] [*]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] [*]1d. Ellipse from 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] [/list] 3. Cyclic Solution: [list] [*]3a. An outer ring of tangent circles: [url]http://www.geogebratube.org/material/show/id/55009[/url] [*]3b. Determine the projection. [*][b]→3c. Final Construction.[/b] [/list]