Properties of Inversion

Inversion across C

1. fixes the circle C,
2. interchanges the inside and outside (5K) of the circle C,
3. is a contraction (5K) on sets outside the circle C,
4. preserves circles S orthogonal (5K) to the inverting circle C,
5. is an involution (5K) (that is, if (x', y') is the inverse of (x, y) across C, then (x, y) is the inverse of (x', y') across C),
6. takes a circle not passing through (a, b) to a circle (5K) not passing through (a, b), and
7. takes a circle passing through (a, b) to a line (5K).

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