HYACINTHOS 27718

[Antreas P.  Hatzipolakis]:

 

Let ABC be a triangle, A'B'C' the pedal triangle of O and and A1B1C1 the pedal triangle of N.

Denote:

A2B2C2 = the pedal triangle of N wrt triangle A1B1C1

The circumcircles of NA'A2, NB'B2, NC'C2 are coaxial,

Second (other than N) intersection?

[Peter Moses]:

Hi Antreas,

a^2 (a^2 b^2-b^4+a^2 c^2+2 b^2 c^2-c^4) (a^10 b^2-4 a^8 b^4+6 a^6 b^6-4 a^4 b^8+a^2 b^10+a^10 c^2-4 a^8 b^2 c^2+2 a^6 b^4 c^2+9 a^4 b^6 c^2-13 a^2 b^8 c^2+5 b^10 c^2-4 a^8 c^4+2 a^6 b^2 c^4+2 a^4 b^4 c^4+3 a^2 b^6 c^4-9 b^8 c^4+6 a^6 c^6+9 a^4 b^2 c^6+3 a^2 b^4 c^6+8 b^6 c^6-4 a^4 c^8-13 a^2 b^2 c^8-9 b^4 c^8+a^2 c^10+5 b^2 c^10:: 

on line: {5,51}.
midpoint of X(11583) and X(16336).

Best regards,
Peter Moses.