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?
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.
for graphical description of inversion.
(In reply to Note to Bractals
The magenta circle is drawn correctly. Circles that are orthogonal to the circle of inversion are mapped into themselves. The only circles whose centers are mapped into the centers of their images are circles of zero radii (ie points).
Posted by Bractals
on 2006-02-24 01:39:21