HYACINTHOS 22624

Antreas P. Hatzipolakis

 

[Antreas]:

 

Let ABC be a triangle.

Denote:

Ab, Ac = the reflections of A in OB, OC, resp.

Na = the NPC center of AAbAc. Similarly Nb, Nc.

The circumcircles of ABC, ANbNc BNcNa, CNaNb

are concurrent at a point Q1

The circumcircles of NaNbNc, NaBC, NbCA, NcAB 

are concurrent at a pint Q2.
(ABC, NaNbNc share the same circumcenter)

Which points are Q1, Q2 ?

APH

 

 

 

[Angel Montesdeoca]:

 

Dear Antreas

 

Q1=X(930)

 

Q2 = (a^2(a^6(b^2+c^2) -

               a^4(3b^4+4b^2c^2+3c^4) +

              a^2(3b^6+2b^4c^2+2b^2c^4+3c^6) 

             -b^8+b^6c^2+b^2c^6-c^8) :...:...)

with (6-9-13)-search number 8.07910137097857081131659206

 

Best regards

 Angel Montesdeoca