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.

I'm not buying any of this yet.  If the center of circle of radius a and the given point are both mapping to a single point after the inversion process, then they were at the same point before the inversion process.

I stick with my previous answer.  The given point is the same distance from the given line as the center of the given circle is from the given line. 

The distance is b.

Posted by Mindrod on 2006-02-23 13:09:58