HYACINTHOS 26901

[Kadir Altintas]

The second intersection, other than G, of the Nagel line IG and X(2) - Altintas hyperbola is the point with simple barycentrics

(b + c)(b^2 + c^2) ::

Which are other properties of this point?

 

Z = X(1)X(2) ∩ X(66)X(71)

= (b+c)*(b^2+c^2) : : (barycentrics)

= (SW+2*s^2)*X(1)-6*(SW+R*r)*X( 2)

= on lines: {1, 2}, {31, 3416}, {37, 6536}, {38, 141}, {66, 71}, {101, 9076}, {190, 4683}, {310, 334}, {313, 561}, {321, 2887}, {345, 4414}, {524, 4722}, {594, 2294}, {740, 3969}, {748, 3966}, {756, 1211}, {1031, 4388}, {1089, 1230}, {1150, 4438}, {1215, 3936}, {1279, 4914}, {1376, 5347}, {1757, 2895}, {1826, 1851}, {1930, 8024}, {1962, 4026}, {1978, 7018}, {2292, 3695}, {2308, 5294}, {2321, 3914}, {3159, 7206}, {3666, 3844}, {3704, 4642}, {3722, 4030}, {3775, 4981}, {3836, 4359}, {3847, 4358}, {3896, 4085}, {3923, 6327}, {3943, 4854}, {3944, 4671}, {3989, 4357}, {3994, 4415}, {3995, 4425}, {4042, 4445}, {4054, 4138}, {4112, 9857}, {4137, 7237}, {4418, 4645}, {4442, 4535}, {7270, 14012}

= midpoint of X(3969) and X(4972)

= reflection of X(2308) in X(5294)

= trilinear pole of the line {826, 8061}

= {X(i),X(j)}-Harmonic conjugate of X(k) for these (i,j,k): (10, 306, 42), (42, 306, 4062), (141, 3703, 38), (321, 2887, 3120), (321, 3773, 6535), (1211, 3932, 756), (2321, 3914, 4365), (2887, 3773, 321), (3120, 6535, 321), (4415, 6057, 3994), (4425, 6541, 3995)

= [ 3.8909941772254580, 1.8370208873082620, 0.5730373242822948 ]

 

César Lozada