On a sheet of paper it is drawn a point $A$ and 2 lines $L_1$ and $L_2$ which intersect outside the sheet in a point B.

Question

On a sheet of paper it is drawn a point $A$ and 2 lines $L_1$ and $L_2$ which intersect outside the sheet in a point B. How one can draw a line $AB$ using only a ruler?

Answer 1

Pappus’ hexagon theorem affords a solution.

Draw lines through $A$ intersecting $L_1$ at $C_1$ and $L_2$ at $C_2$, respectively:

Through $C_1$ draw a line intersecting $AC_2$ at $D_1$ and $L_2$ at $E_2$, and similarly for $C_2$:

Let $F$ be the intersection of $D_1E_1$ and $D_2E_2$:

Points $A$, $B$ and $F$ are colinear.

In practice, it requires a bit of care to ensure that all of these points remain on the paper and within the length of the ruler.