Inversion in a circle
Our version of Apollonius's Theorem led us to make the
We denote the inverse by iC(P), or, if C is obvious, by P'.
Inversion is built into Cabri.
There are, however, two problems:
These occur since we cannot have
OO.OP = r2.
|To motivate the way we resolve this, you can use the CabriJava pane
to investigate what happens as P approaches O.
You should conclude that P' moves rapidly out along the ray OP.
In an intuitive sense, P' approaches infinity.
In fact, when P reaches O, The ray (and hence P') are undefined.
|See The extended plane|
|Main Inversive Page|