Three masses are constrained to lie on the edges of a triangle.  Equal constant force actuators (with force F) are attached to each pair of masses.  When this system finds equilibrium, the potential energy will be at a minimum.  However, the PE in each actuator is simply F times L, where L is the length of the actuator.

Hence minimum PE is achieved when the masses sit at the vertices of the minimum perimeter inscribed triangle.

Press Show to see the normals to the sides of the triangle at the location of the masses.