We're given three random points on the plane: $O,A$ and $B$
Our goal is to construct the equilateral triangle $\triangle XYZ$, such that $O$ is its centroid and points $A$ and $B$ lie on the sides of $\triangle XYZ$ as in the image below
I know we can find a locus for vertice $X$ on the circle that sees segment $AB$ through an angle of 60 degrees.
I need some other relation which I simply cannot find. I tried to think about the areas of triangles $\triangle OAB, \triangle OAX$ and $\triangle OBX$ but to no avail. Those areas are not a simple linear combination of each other. I just don't know what to do, I would like some relationship between $O$ and $X$ (or any other hint on how to solve it)