# Inversion in the plane: inversion

### 13.15.7 Inversion in the plane: inversion

See Section 14.14.7 for inversions in space.

Given a circle C with center P and radius r, the inversion of a point A with respect to C is the point A′ on the ray PA satisfying PA·PA′ = r2.

The inversion command creates an inversion.

- inversion takes two mandatory arguments and one optional argument:
  - P, a point (the center of the inversion).
  - r, a real number (the radius).
  - Optionally, G, a geometric object.
- inversion(P,r) returns a new command which performs the inversion.
- inversion(P,r,G) returns and draws the inversion of G.

#### Examples.

- Input:

  inver:= inversion(i, 2)
  inver(circle(1+i,1))

  Output:
  then:
  inver(circle(1+i,1/2))
  Output:
- Input:
  inversion(i, 2, circle(1+i,1))
  Output:
  Input:
  inversion(i, 2, circle(1+i,1/2))
  Output: