Let \(ABCD^{}_{}\) be a tetrahedron with \(AB=41^{}_{}, AC=7^{}_{}, AD=18^{}_{}, BC=36^{}_{}, BD=27^{}_{}\), and \(CD=13^{}_{}\), as shown in the figure. Let \(d^{}_{}\) be the distance between the midpoints of edges \(AB^{}_{}\) and \(CD^{}_{}\). Find \(d^{2}_{}\).

(第七届AIME1989 第12题)