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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.

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

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.)
Some Thoughts Note to Bractals | Comment 18 of 32 |

Nice problem.  Am I reading it wrong?

Please check the position of the center of the magenta circle shown on your drawing at www.geocities.com/bractals/inv.jpg . I believe the center of the magenta circle must be located on the circumference of the circle of inversion in order to map onto itself. 

Let C be the center of the magenta circle, then |OC|*|OC'| = k2
only if |OC| = k.

(Because C and C' are located at the same position.)

Edited on February 23, 2006, 9:23 pm
  Posted by Mindrod on 2006-02-23 21:09:01

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