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 Inversion Distance (Posted on 2006-02-21)
A circle (of radius a), a line, and a point are mapped by inversion into two concentric circles and the center of those concentric circles. If the distance from the given circle's center to the line is b, then what is the distance from the point to the line?

Inversion Defined:

Let O be the center of a circle of radius k. An inversion with respect to circle O is a mapping f:R2 -> R2 such that for all P in R2 (not O), P' = f(P) lies on ray OP and
|OP'||OP| = k2.

See www.geocities.com/bractals/inv.jpg

for graphical description of inversion.

 See The Solution Submitted by Bractals Rating: 2.8000 (5 votes)

 Subject Author Date re(2): Solution: I think I have it right now. Mindrod 2006-02-26 12:47:38 re: Solution: I think I have it right now. Eric 2006-02-26 04:11:53 Solution: I think I have it right now. Mindrod 2006-02-25 22:40:47 re(3): problem resolved Dej Mar 2006-02-25 20:33:31 re(6): Note to Bractals Dej Mar 2006-02-25 16:20:01 re(5): Note to Bractals Eric 2006-02-25 14:13:42 re(4): Note to Bractals and Eric Mindrod 2006-02-25 14:12:59 re(3): Note to Bractals Bractals 2006-02-25 12:08:38 re(4): Note to Bractals Dej Mar 2006-02-25 05:58:05 re(3): Note to Bractals Eric 2006-02-25 03:08:26 re(2): Note to Bractals Mindrod 2006-02-24 20:47:28 re(2): Note to Bractals Mindrod 2006-02-24 20:31:54 re: Note to Bractals Bractals 2006-02-24 01:39:21 re: Note to Bractals Eric 2006-02-23 23:34:25 Note to Bractals Mindrod 2006-02-23 21:09:01 re(2): Disagreement resolved Mindrod 2006-02-23 21:06:39 re: Disagreement Eric 2006-02-23 16:13:58 Disagreement Mindrod 2006-02-23 13:09:58 re: Algebraic solution goFish 2006-02-23 03:23:40 Algebraic solution Tristan 2006-02-22 21:58:05 re(3): problem resolved - yep goFish 2006-02-22 17:31:55 re(2): problem resolved Eric 2006-02-22 17:08:39 re: problem goFish 2006-02-22 11:05:26 problem Charlie 2006-02-22 10:25:11 re: Now I have it. Error? goFish 2006-02-22 10:14:05 Clarification required goFish 2006-02-22 04:58:51 Now I have it. Eric 2006-02-22 02:03:52 re: special case? spoiler, perhaps Eric 2006-02-22 01:50:11 re: special case? spoiler, perhaps Mindrod 2006-02-21 23:08:27 special case? spoiler, perhaps Mindrod 2006-02-21 22:54:07 How do I explain this? Eric 2006-02-21 18:25:24 d3.5? Percy 2006-02-21 18:23:55

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