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21998TCS: P14

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  • Antreas
    Aug 16, 2013
    • 0 Attachment
      [Hatzipolakis - Lozada]

      Let ABC be a triangle and AhBhCh, AoBoCo
      the pedal triangles of H, O, (orthic,medial tr.) resp.


      Haa, Hbb, Hcc = the orthogonal projections of H
      on OAo, OBo, OCo, resp.

      Hab, Hac = the orhogonal projections of Haa
      on OBo, OCo, resp.

      Hbc, Hba = the orthogonal projections of Hbb
      on OCo, OAo, resp.

      Hca, Hcb = the orthogonal projections of Hcc
      on OAo, OBo, resp.

      1.1. HabHac, HbcHba, HcaHcb concur at a point H*

      1.2. The Euler lines Ma,Mb,Mc of HaaHabHac, HbbHbcHba,
      HccHcaHcb, resp. concur at H*


      H*=((b^2+c^2)*a^6-(3*(c^4+b^4))*a^4+(b^2+c^2)*(3*b^4+3*c^4-2*b^2*c^2)*a^2-(b^4+4*b^2*c^2+c^4)*(b^2-c^2)^2)*a : : (trilinears)

      H*=complement of X(185)