The conics of Lucas' configuration (Q1025798)

The Lucas configuration consists of a triangle and three special squares with edges on the triangle's sides. The twelve square vertices can be divided into two groups of six points such that the points of one group lie on a conic section. An additional assumption on the orientation of the squares guarantees that one of these conics is even an ellipse. The proof consists of a straightforward calculation. Other geometric properties of the Lucas configuration have attained earlier attention, see \textit{I.~Panakis} [Plane Trigonometry, Vol II. Private publication, Athens (1973)] or \textit{A.~P.~Hatzipolakis} and \textit{P.~Yiu} [Am. Math. Mon. 108, 444--446 (2001; Zbl 0981.51018)].