HYACINTHOS 25324

 

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle.

Denote:

A', B', C' = the reflections of O in BC, CA, AB, resp.

A", B", C" = the circumcenters of IBC, ICA, IAB, resp.

The NPCs of AA'A", BB'B", CC'C" are coaxial.

The 1st point of concurrence is the common midpoint of AA', BB', CC' = the N.

The 2nd one?

[A', B', C' = reflections of A, B, C in N]

 

[Angel Montesdeoca, Hyacinthos 25322]

( a^3 (b+c)+a^2 (b-c)^2-a (b^3+c^3)-(b^2-c^2)^2:...:...) ,
with (6-9-13)-search numbers (7.36449423012126,5. 30642808102669,-3. 43201383424391).
Is the midpoint of X(i) and X(j) for these {i,j}: {1,5080}, {36,5057}, {484,5180}, {3583,4511}.