# Pole and polar: pole polar

### 13.17.5 Pole and polar: pole polar

Given a circle centered at O, a point A is a pole and a line L is the corresponding polar if L is the line passing through the inversion of A with respect to the circle (see Section 13.15.7) passing through the line OA.

The polar command finds the polar of a point.

- polar takes two arguments:
  - C, a circle.
  - A, a point.
- polar(C,A) returns and draws the polar of the point A with respect to C.

#### Example.

Input:

polar(circle(0,1),(i+1)/2)

Output:

The pole command finds the pole of a line.

- pole takes two arguments:
  - C, a circle.
  - L, a line
- pole(C,L) returns and draws the pole of the line L with respect to C.

#### Examples.

- Input:
  pole(circle(0,1),line(i,1))
  Output:
- Input:
  affix(pole(circle(0,1),line(i,1)))
  Output:

  1+i