HYACINTHOS 21518

Antreas P. Hatzipolakis

 

Let ABC be a triangle, (N),(N1),(N2),(N3) the NPCs of ABC,NBC,NCA,NAB, resp. [concurrent at pN]. The NPCs of the triangles N1N2N3, NN1N2, NN2N3, NN3N1 concur at point ppN on the Euler Line of ABC.

Coordinates of ppN?

Generalization:

Let ABC be a triangle, P a point, (N),(N1),(N2),(N3) the NPCs of ABC, PBC, PCA, PAB resp. [concurrent at pP]. If P is on the Euler line of ABC, then the NPCs of N1N2N3, PN1N2, PN2N3, PN3N1 concur at point ppP on the Euler Line of ABC.

True??

APH