In Euclid's first geometry proposition, he constructs an equilateral triangle given an arbitrary line segment. I was wondering if it was possible to prove this straight from Tarski's axioms for geometry (see https://en.wikipedia.org/wiki/Tarski%27s_axioms). This amounts to proving the following statement:
Given points $a,b,c,d$ such that $Babc$ and $Bbcd$ prove that there exists a point $x$ such that $ax\equiv ac$ and $dx\equiv db$.
I am not really sure on how to get a nontrivial point (meaning not some arbitrary point) outside of the line that $a,b,c,d$ lie in.