INVERSION - Simple Cases

Up until now we have examined various interesting configurations, mostly relating to the circle. Now things get even more interesting as we use our knowledge to develop techniques for finding new results.

Let $\Gamma$ denote a fixed given circle with centre $O$ and radius $a$. We have defined points $P,P^{\prime }$ to be inverse if $O,P,P^{\prime }$ are collinear and

  .

The circle $\Gamma$ (Gamma) is called the circle of inversion, and a is the radius of inversion. 

Now if point $P$ moves along a certain curve, the inverse point $P^{\prime }$ will also determine a curve – the inverse of the original curve. Inversion is sometimes called «reflection in a circle».

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