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.

Am I correct in reading this question as follows:

There are three objects a circle A with radius a, a line L and a point P all of which are mapped by inversion in a fourth object, an undefined circle of inversion.  That is: the definition of inversion given is merely additional information?

In this case the answer is likely to be independent of the radius of the circle of inversion.

ps It may be helpful to some readers to note that the straight line L always maps to a circle which passes through the centre of the circle of inversion.

 

Edited on February 22, 2006, 4:59 am

Posted by goFish on 2006-02-22 04:58:51