HYACINTHOS 26540

[Antreas P. Hatzipolakis]:

 

 

Let ABC be a triangle, A'B'C' the pedal triangle of O and IaIbIc the antipedal triangle of I.

Denote:

M1, M2, M3 = the midpoints of IA', IB', IC', resp.

Ma, Mb, Mc = the midpoints of IaA', IbB', IcC', resp

M1M2M3, MaMbMc are bilogic (Perspective and orthologic).

Perspector, orthologic centers?

 

 

[César Lozada]:

1)      Perspector: X(1125)

 

2)      Orthologic centers:

 

Q( Ma->M1 ) = X(3579)

 

Q( M1->Ma) =

= a*(2*a^3+(b+c)*a^2-2*(b^2+13* b*c+c^2)*a-(b+c)*(b^2+10*b*c+ c^2)) : :  (barys)

=  X(1)+3*X(3646) = 5*X(1)+3*X(4866) = X(3296)-5*X(3616) = 5*X(3646)-X(4866)

= On lines: {1, 210}, {551, 5302}, {1001, 13624}, {1125, 3579} , {3296, 3616}, {3634, 3813}, {3647, 11281}, {5550, 11024}, {5919, 11524}

= [ 2.523844846890819, 1.85394392084552, 1.192313376603254 ]

 

César Lozada

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