Given a smooth Jordan curve and a cyclic quadrilateral (a cyclic quadrilateral is a quadrilateral that can be inscribed in a circle) we show that there exist four points on the Jordan curve forming the vertices of a quadrilateral similar to the one given. The smoothness condition cannot be dropped (since not all cyclic quadrilaterals can be inscribed in all triangles), while the cyclicity is necessary (since the circle is itself a smooth Jordan curve). The proof involves some results in symplectic topology. No prior knowledge assumed. \\ \\ Joint work with Josh Greene.