Yes indeed, equal strength zero rest length springs will give the average of the 3 points.
This is conveniently the same as the point which minimises the sum of the squared lengths.

I should also add that in the question the poster asked for all lines pulling with the same force, which isn’t strictly what’s happening in my first answer, because the more stretched springs are under more tension. For the forces to be the same magnitude we’d want not springs but ConstantTension goals, like this:

The point then ends up so that the 3 angles are all 120°
which is also the point which minimises the sum of the lengths (instead of their squares like with springs)