Feuerbach by using complex numbers (Q2831688)

After an introductory paragraph from the editor of the journal Nieuw Archief voor Wiskunde, the author provides a proof of the following theorem of Feuerbach (1822), grounded on working with complex numbers as provided by \textit{F. Morley} and \textit{F. V. Morley}, father and son, in their book [Inversive geometry. London: G. Bell \& Sons (1933; JFM 59.0603.01; Zbl 0009.02908)] (reprint Dover, 2014 from the original, p. 191):NEWLINENEWLINE Theorem: The nine-point-circle of a triangle touches the inner-circle and each of the three outer-circles of that triangle (each of the last four circles touches the sides of the triangle).NEWLINENEWLINE The way, the author and the Morleys treat Feuerbach's theorem are the same, but the author's treatment is far more suited for a general mathematical public.NEWLINENEWLINE As Morleys' isosceles triangle theorem is only slightly mentioned in the text of the author, he also mentions that a proof of that theorem can be found in the book of the Morleys on page 244.