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Inversion Distance (Posted on 2006-02-21) Difficulty: 3 of 5
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.


for graphical description of inversion.

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

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): Solution: I think I have it right now.Mindrod2006-02-26 12:47:38
re: Solution: I think I have it right now.Eric2006-02-26 04:11:53
SolutionSolution: I think I have it right now.Mindrod2006-02-25 22:40:47
re(3): problem resolvedDej Mar2006-02-25 20:33:31
re(6): Note to BractalsDej Mar2006-02-25 16:20:01
re(5): Note to BractalsEric2006-02-25 14:13:42
re(4): Note to Bractals and EricMindrod2006-02-25 14:12:59
re(3): Note to BractalsBractals2006-02-25 12:08:38
re(4): Note to BractalsDej Mar2006-02-25 05:58:05
re(3): Note to BractalsEric2006-02-25 03:08:26
re(2): Note to BractalsMindrod2006-02-24 20:47:28
re(2): Note to BractalsMindrod2006-02-24 20:31:54
re: Note to BractalsBractals2006-02-24 01:39:21
re: Note to BractalsEric2006-02-23 23:34:25
Some ThoughtsNote to BractalsMindrod2006-02-23 21:09:01
Solutionre(2): Disagreement resolvedMindrod2006-02-23 21:06:39
re: DisagreementEric2006-02-23 16:13:58
SolutionDisagreementMindrod2006-02-23 13:09:58
re: Algebraic solutiongoFish2006-02-23 03:23:40
SolutionAlgebraic solutionTristan2006-02-22 21:58:05
re(3): problem resolved - yepgoFish2006-02-22 17:31:55
re(2): problem resolvedEric2006-02-22 17:08:39
re: problemgoFish2006-02-22 11:05:26
Some ThoughtsproblemCharlie2006-02-22 10:25:11
re: Now I have it. Error?goFish2006-02-22 10:14:05
Clarification requiredgoFish2006-02-22 04:58:51
Now I have it.Eric2006-02-22 02:03:52
re: special case? spoiler, perhapsEric2006-02-22 01:50:11
re: special case? spoiler, perhapsMindrod2006-02-21 23:08:27
Some Thoughtsspecial case? spoiler, perhapsMindrod2006-02-21 22:54:07
SolutionHow do I explain this?Eric2006-02-21 18:25:24
d3.5?Percy2006-02-21 18:23:55
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