HYACINTHOS 25472

[Antreas P. Hatzipolakis]:

Let ABC be a triangle, AhBhCh the pedal triange of H and N' the Poncelet point of ABCN

(ie the point the NPCs of ABC, NBC, NCA, NAB are concurrent at).

Denote:

hA = the second intersection of AhN' and the NPC of NBC
hB = the second intersection of BhN' and the NPC of NCA
hC = the second intersection of ChN' and the NPC of NAB

ABC, hAhBhC are orthologic.

 

[César Lozada]:

Orthologic centers:

 

Z(A->hA) =  cos(B-C)*sec(2*(B-C))/(1-2* cos(2*A)) : : (trilinears)

= On line: {252,5449}

= isogonal conjugate of {4,1510}/\{54,5946}

= [ 1.906612339547154, 0.77749424457911, 2.222424309715539 ]

 

Z(hA->A) = X(143)

 

César Lozada