HYACINTHOS 24847

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle and P a point.

Denote:

Na, Nb, Nc = the NPC centers of PBC, PCA, PAB, resp.

Naa, Nab, Nac = the reflections of Na in PA, PB, PC, resp.

Nba, Nbb, Nbc = the reflections of Nb in PA, PB, PC, resp.

Nca, Ncb, Ncc = the reflections of Nc in PA, PB, PC, resp.

La, Lb, Lc = the Euler lines of NaaNabNac, NbaNbbNbc, NcaNcbNcc, resp. (concurrent at P)

Which is the locus of P such that the parallels to La, Lb, Lc through A, B, C are concurrent?

I lies on the locus (point of cncurrence = I)

O lies on the locus (point of concurrence on the circumcircle)

[Peter Moses]:

Hi Antreas,

 

>Which is the locus of P such that the parallels to La, Lb, Lc through A, B, C are concurrent?
K003, degree 8 through {13,14,110}, degree 6 through {13,14}.

 

>O lies on the locus (point of concurrence on the circumcircle)
O –> X(1141).

H –> X(5663).

 

Best regards,

Peter Moses.