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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: ( Back to comment list | You must be logged in to post comments.)
re: Note to Bractals | Comment 20 of 32 |
(In reply to Note to Bractals by Mindrod)

The magenta circle is drawn correctly. Circles that are orthogonal to the circle of inversion are mapped into themselves. The only circles whose centers are mapped into the centers of their images are circles of zero radii (ie points).
  Posted by Bractals on 2006-02-24 01:39:21

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