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Original Research Article In this paper we discuss a kind of symmetric configuration for planar concave 5-body problem with four of the five bodies on the vertex of an isosceles trapezoid and the other on the axis of symmetry inside the isosceles trapezoid. Then we give a special case to prove that there exist a set of positive masses to make this configuration a central configuration when the inner body not coincident with the center of mass.

A Special Case of Central Configuration for Planar Concave 5-body Problem with Newtonian Potentials