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: Solution: I think I have it right now. by Eric)

Thanks, Eric, you are right.  I just checked your corrections against my notes and they match. 

It is funny how I managed to miss the "c" in both places. But I can see why it happened. 

Thanks for pointing this out.  I'll edit my original post so it doesn't confuse anyone who is trying to follow along.

Posted by Mindrod on 2006-02-26 12:47:38