@TedShifrin @BalarkaSen @Alizter Let $A=\{(0,0), (1, 0)\}$. $a \in \mathbb{R}$ is contructible if the point $(a,0)$ is constructible from $A$.
We take the line $(\epsilon)$ that goes through the points $P_1=(0,0)$ and $P_2=(1,0)$, which is constructible.
We take the circle with center $(0,0)$ and radius $1$ and the circle with center $(1,0)$ and radius $1$.
The intersection points of the circles are $P$ and $Q$.
We take the line $P_1P$ and $P_2P$.
We take the line $PQ$ that goes through the line $(\epsilon)$ at the point $M$.
