- Let ABC be a triangle, P a point and HaHbHc the
orthic triangle of ABC.
Let La, Lb, Lc be the parallels to HbHc, HcHa, HaHb
resp. through P.
Lab = La /\ AB, Lac = La /\ AC
Ab = Orthogonal Projection of Lab on PPa
Ac = Orthogonal Projection of Lac on PPa
A' = BAb /\ CAc. Similarly B', C'.
Which is the locus of P such that ABC, A'B'C' are perspective?
PS. I found a cubic whose the equation has the xyz term,
but I don't know if decomposes or not.