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The present study deals with the applications of the planar Newtonian four-body problem to the different central configurations. The basic concept of central configuration is that the vector force must be in the direction of the position vector so that the origin may be taken at the centre of mass of the four bodies and the force towards the position vector multiplied by corresponding inverse mass is directly proportional to the position vector relative to the centre of mass. For applying the Newtonian four body problem to the central configuration, the equations of motion of four bodies have been established in inertial frame. By the methods of previous authors, some mathematical tools of the planar problem have been developed and by using them, the Newtonian four-body problem have been reduced to central configuration. All the previously generated mathematical models depend upon the directed areas, weighted directed areas and position vectors of the centre of the bodies. With the help of these models some conditions have been established, which show that the origin is located at the centre of mass of the system. Finally these conditions have been used to some particular cases of concave configuration, convex configuration and symmetric configuration to generate some tools which will be helpful for further researches of this field. [ABSTRACT FROM AUTHOR]