Bicentric quadrilateral central configurations

摘要

A bicentric quadrilateral is a tangential cyclic quadrilateral. In a tangential quadrilateral, the four sides are tangents to an inscribed circle, and in a cyclic quadrilateral the four vertices lie on a circumscribed circle. In this paper, we classify all planar central configurations of the 4-body problem, where the four bodies are at the vertices of a bicentric quadrilateral.