## A note on inversion through a circle:

Let **C** be a circle, with center **o**. Then for any point **a**,
at distance *s* from **o**, the inverse **a-1**
is the point that lies on the line **ao** at distance 1/**s **from
**o**.

If **a** is *inside* **C**, then **a-1** will be *outside ***C**

If **a** is *outside* **C**, then **a-1** will be *inside ***C**

If **a** is *on ***C**, then **a-1** = ** a **

And if **a**=**o**, then **a-1** is undefined (or if you prefer, is
the point at infinity)

Inversion has many beautiful properties. For example, circular arcs, when inverted,
are still circular arcs. The two shapes above are inverses of one another. **You
can download an interactive version
of this image!**

(To use the downloaded interactive image, you must have *Geometer's Sketchpad*.
A demo version is available
here)