32. Tangency Problem of Apollonius

This is problem #32 in Heinrich Dorrie's [i]100 Great Problems of Elementary Mathematics.[/i]

Uses the following constructions: Power Center: [url]http://www.geogebratube.org/material/show/id/33929[/url] Similarity Points: [url]http://www.geogebratube.org/material/show/id/34182[/url] Pole and Polar: [url]http://www.geogebratube.org/material/show/id/34578[/url] I found this problem difficult; the solution presented here does not deviate from the text. _____________________________ [list=1] [*][b]Geometric Solution[/b] [*]Differential Solution: a. Seek model (one circle): [url]http://www.geogebratube.org/material/show/id/34821[/url] b. Solution, v.1: [url]http://www.geogebratube.org/material/show/id/34855[/url] c. Solution v.2, improved: [url]http://www.geogebratube.org/material/show/id/35386[/url] [/list]