HYACINTHOS 26798

[Antreas P. Hatzipolakis]:

 

 

Let ABC be a triangle.

Denote:

Na, Nb, Nc = the NPC centers of NBC, NCA, NAB, resp.

The reflections of ONa, ONb, ONc in NA, NB, NC, resp. are concurrent.

[César Lozada]:

At:

Q = X(5)X(252) ∩ X(155)X(195)
= (2*cos(2*A)-4)*cos(B-C)+(2*cos(A)+4*cos(3*A))*cos(2*(B-C))+(2*cos(2*A)-2)*cos(3*(B-C))-cos(5*A)+cos(A)+5*cos(3*A) : : (trilinears)
= 8*S^4+(24*R^4+(5*SA-17*SW)*R^2+2*(3*SA-SW)*(SA-SW))*S^2+(13*R^2-7*SW)*(SA-SW)*R^2*SA : : (barycentrics)
= On lines: {5, 252}, {155, 195}, {546, 1263}, {3091, 3459}, {5501, 14140}
= [ -0.970174699886774, -2.95414689596268, 6.133616040598592 ]

César Lozada