I'm learning hyperbolic geometry by following Prof NJ Wildberger videos on YouTube. So far I know how to find the dual of a point (which is a line) geometrically (using pen, paper, and ruler). Here's an example:
In the given example, I started with point A and constructed its dual-line, FG. This is the process:
- Find two arbitrary lines that cross the circle in two points (each) while passing through point A (here: AB and AC).
- Find the other two intersects of the lines and the circle, D and E.
- Construct the quadrilateral and the diagonal lines by connecting all the combinations of B, C, D, and E (i.e. BC, BE, CD, and EF - we already had BD and CE).
- This will give you points F and G and connecting them will give you the dual line of A.
Now my question is, how can I find A if I was given FG? I know how to find A algebraically but I'm interested in the geometrical approach.