Anallagmatic cubics through quadratic involutive transformations. I (Q1312236)

Generalizing the study undertaken in J. Geom. 34, No. 1/2, 152-171 (1989; Zbl 0664.51018), the author considers -- for an arbitrary triangle \(ABC\), a point \(F\) different from \(A\), \(B\), \(C\), and a point \(D\) not on the sides of \(ABC\) -- the locus \(K_{F,D}\) of all points \(P\) for which \(P\), \(T(P)\) and \(F\) are collinear, where \(T\) is a certain quadratic involutive transformation determined by \(ABC\) and \(D\). \(K_{F,D}\) is a cubic and the author points out that there are 40 special points and 32 tangent lines associated to it.