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Isosceles trapezoid central configurations of the Newtonian four-body problem

We use a simple direct and basic method to prove that there is a unique isosceles trapezoid central configuration of the planar Newtonian four-body problem when two pairs of equal masses are located at adjacent vertices of a trapezoid. Such isosceles trapezoid central configurations are an exactly one-dimensional family. Explicit expressions for masses are given in terms of the size of the quadrilateral.