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Neuberg, Euler lines and NPCs

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  • Antreas
    Let ABC be a triangle, P be a point on the Neuberg cubic, and S the point of concurrence of the Euler Lines of ABC, PBC, PCA, PAB. 1. Are the NPCs of ABC, PBC,
    Message 1 of 1 , Feb 14, 2013
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      Let ABC be a triangle, P be a point on the Neuberg cubic,
      and S the point of concurrence of the Euler Lines of ABC,
      PBC, PCA, PAB.

      1. Are the NPCs of ABC, PBC, PCA, PAB, SBC, SCA, SAB concurrent?
      (ie the r. circumhyperbola ABCP is also passing through S ?)

      2. Let N1, N2, N3 be the NPC centers of PBC, PCA, PAB
      and Na,Nb,Nc of SBC, SCA, SAB.

      Are the triangles N1N2N3, NaNbNc perspective?

      Which are the perspectors if P is some simple
      point ie P = I, Fermat_1, Fermat_2 ?

      3. Let H1, H2, H3 be the orthocenters of PBC, PCA, PAB
      and Ha, Hb, Hc of SBC, SCA, SAB.

      Are the triangles H1H2H3, HaHbHc perspective?

      4. In general: Qa, Qb, Qc, Q1, Q2, Q3 = same points on the
      Euler lines of PBC, PCA, PAB, SBC, SCA, SAB.

      Are the triangles QaQbQc, Q1Q2Q3 perspective?

      APH
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