Consider two continuous embeddings of the real line into the plane that are disjoint and periodic under translation by i.  Tao suggested a variation of the square peg problem for Jordan curves, and conjectured that every such pair of curves inscribes a square. I will talk about how we can generalize Tao's conjecture to other quadrilaterals. In particular, we prove a pair of disjoint, periodic curves inscribe every isosceles trapezoid using Lagrangian Floer homology.