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.

(In reply to re: Note to Bractals by Eric)

Okay.  So if the point at the center of the "image" of the circle is not the true center of that circle, where is the true center? And how can two circle "images" be considered concentric if their true centers are not located at the same point?

I know the definition of "concentric circles" in the "real" world.  How do you define "concentric circles" in the "image" world?

Posted by Mindrod on 2006-02-24 20:47:28