How I construct a segment $a^2$?

Question

The length of a segment is given. How can we construct a segment equal to the square of the given segment?

Answer 1

Use this construction. BTW, it can also be used to multiply $a$ times $b$:

The green lines are parallel. The blue lines are any two that form an angle. You need a unit length as well, of course.

Answer 2

Carry out the inversion of the point $1$ on the $x$-axis with respect to the circle of radius $a$ centered at the origin.

Answer 3

Revised attempt:

1) Construct a $\triangle DBC$ with :

$|DB|=1;$ $ \angle BDC =90°$; $|DC|=a$ .

2) Construct a right angle at $C$, with one leg $BC$.

The other leg of this angle intersects $BD$

at $A$, I.e $\angle BCA =90°$.

3) We have :

$|AD| \cdot 1 = a^2.$