HYACINTHOS 22628

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.

 

APH

 

[Angel]:

The  orthology center of ABC with respect to NaNbNc is X(1141) on the circumcircle. of  ABC.

 

The  orthology center of NaNbNc with respect to ABC (on the circumcircle of NaNbNc) is

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

3a^4(b^4+c^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 5.485624417414120257712782094

 

Best regards

 Angel Montesdeoca

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http://amontes.webs.ull.es/otrashtm/HechosGeometricos.htm#HG121014