Michal Rol\'{i}nek and Le Anh Dung, The Miquel points, pseudocircumcenter, and Euler-Poncelet point of a complete quadrilateral,
Forum Geometricorum, 14 (2014) 145--153.

Abstract. We prove over 40 similarities in the configuration of a complete quadrilateral and the Miquel points. Then we introduce a generalized circumcenter and prove a theorem on the Euler-Poncelet point.

[ps file] [pdf]