HYACINTHOS 26764

[Antreas P. Hatzipolakis]:

Let ABC be a triangle and HaHbHc, OaObOc the pedal triangles of H, O, resp.

Denore:

H1H2H3, O1O2O3 = the orthic triangles of HaHbHc, OaObOc, resp.

 

Ma, Mb, Mc = the mdpoints of H1O1, H2O2, H3O3, resp.

HaHbHc, MaMbMc are orthologic.

[César Lozada]:

Ma->Ha = X(5462)

Ha->Ma = X(137)X(143) ∩ X(570)X(1506)

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

= (S^2+SB*SC)*(3*S^2-SA^2)*(3* SA^2-2*(R^2+SW)*SA+4*S^2-SW^2+ 2*R^2*SW) : : (barycentrics)

= On cubic K416 and lines: {137, 143}, {546, 6146}, {570, 1506}, {3518, 14129}

= {X(137), X(10216)}-Harmonic conjugate of X(143)

= [ 0.097049936430004, 0.07878748534386, 3.541327021394010 ]

 

César Lozada