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?

Antreas

PS. I found a cubic whose the equation has the xyz term,

but I don't know if decomposes or not.

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