HYACINTHOS 26420

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle.

Denote:

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

Ab, Ac = the orthogonal projections of N on BA', CA', resp.

La = the Euler line of NAbAc. Similarly Nb,Nc

La, Lb ,Lc are concurrent

 

 

[César Lozada]:

 

Q = midpoint of X(195) and X(930)

= (cos(B-C)^2-(cos(2*A)-1/2)^2)* ((cos(2*A)+1/2)*cos(B-C)+cos( A)*(cos(2*(B-C))+1)+cos(3*A)): : (trilinears)

= On lines: {5,6343}, {125,128}, {137,5501}, {195,930}, {6150,6592}

= midpoint of X(i) and X(j) for these {i,j}: {5,6343}, {195,930}

= reflection of X(137) in X(8254)

= [ -2.509138733929111, 12.93465249265628, -4.156030905041147 ]

 

César Lozada