A static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and bilaterally supported along a single periphery arc, the remaining part of the boundary being free. The contact reaction is assumed to be formed by a distributed reaction force accompanied by a distributed moment with radial axis. This plate problem is formulated in terms of an integral equation of the Prandtl type, supplemented by a vertical and a rotational equilibrium condition. It is shown that the Prandtl equation coupled to the equilibrium condition possesses a unique solution in a proper scale of weighted Sobolev-type spaces, with certain smoothness properties, and that no solution exists if the distributed moment is absent. Finally, the behaviour of the solution at the endpoints of the support is clarified.