Moduli spaces of bicentric quadrilaterals

We deal with planar moduli spaces of polygonal linkages arising from a poristic family of bicentric polygons. For bicentric quadrilaterals, we describe the topological types of moduli spaces in poristic families and find the absolute maximum and minimum of oriented area in the union of moduli spaces. Similar results are obtained for poristic quadrilaterals associated with a pair of confocal ellipses. In conclusion we outline some research perspectives suggested by our results.