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 Now I have it. by Eric)

Eric, you write

"we already know that the distance from s to (k^2)/2s is b "

This is not correct. b is the distance from the centre of the given circle to the line NOT as you have assumed from the centre of the image of the given circle to the line.

Posted by goFish on 2006-02-22 10:14:05