Moduli spaces of bicentric quadrilaterals (Q906456)

A polygon in the plane is bicentric if its vertices are inscribed in a circle \(C_1\) and its edges are tangent to a circle \(C_2\) contained in \(C_1\). A bicentric \(k\)-gon with circles \(C_1\) and \(C_2\) belongs to a whole family of bicentric \(k\)-gons with the same circles, called the poristic family of the pair \((C_1,C_2)\). For bicentric quadrilaterals, the paper describes the topological type of moduli spaces in poristic families and determines the absolute maximum and minimum of oriented area in the union of moduli spaces. Similar results are also obtained for poristic families of quadrilaterals inscribed in, or circumscribed about, the ellipses in a pair of confocal ellipses.