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21971RE: [EMHL] NPC. locus.

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  • César Lozada
    Apr 17, 2013
    • 0 Attachment
      Yes, they are concyclic.



      The center X of the circle has trilinears:

      2*cos(A)+4*sin(3*A/2)*cos(B/2-C/2)+ cos(B-C)+2 : :



      ETC search: 2.387773069046934.., 2.38593313995937.., 0.886815506990847..



      X=Midpoint of X(I),X(J) for these (I,J):

      (1,500)




      X lies on line X(I),X(J) for these (I,J):

      (1,30), (3,81), (5,581), (21,323), (30,79), (58,5428), (79,500),
      (140,3216),

      (186,2906), (237,1896), (285,1082), (358,1882), (386,549), (500,554),
      (511,1385),

      (550,991), (554,1081), (1036,4022), (1081,1464), (1154,2646), (1464,1717),


      (1675,4280), (1717,1836), (1836,3058), (2071,4309), (2072,3746),
      (2771,3743),

      (2943,4341), (3058,3649), (3108,3784), (3649,3655), (3655,3656),
      (3656,3782),

      (3704,3990), (3782,4654), (4654,4854), (4854,5160), (5160,5434),
      (5434,5441)



      Regards

      César Lozada



      _____

      De: Hyacinthos@yahoogroups.com [mailto:Hyacinthos@yahoogroups.com] En nombre
      de Antreas Hatzipolakis
      Enviado el: Miércoles, 17 de Abril de 2013 05:34 a.m.
      Para: Hyacinthos
      Asunto: Re: [EMHL] NPC. locus.





      A CIRCLE:

      Let ABC be a triangle, A'B'C' the cevian triangle of I and N1, N2, N3
      the NPC centers of IB'C', IC'A', IA'B', resp.

      The points I, N1,N2,N3 are concyclic.

      Center of the circle?

      LOCUS:

      Let ABC be a triangle, P a point, A'B'C' the cevian triangle of P and N1,
      N2, N3
      the NPC centers of PB'C', PC'A', PA'B', resp.

      Which is the locus of P such that the points P, N1,N2,N3 are concyclic ?

      Antreas

      On Wed, Apr 17, 2013 at 1:43 AM, Antreas <anopolis72@...
      <mailto:anopolis72%40gmail.com> > wrote:

      > **
      >
      >
      > Let ABC be a triangle and P a point.
      >
      > Which is the locus of P such that the NPC center of PBC
      > lies on the line AP ?
      >
      > Ceva triangle variation:
      >
      > Let ABC be a triangle, P a point and A'B'C'
      > the cevian triangle of P.
      > Which is the locus of P such that the NPC center
      > of PB'C' lies on the line APA' ?
      > (The I is on the locus)
      >
      > APH
      >
      >
      >
      >
      >

      http://anopolis72000.blogspot.com/

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