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Orthocenters Diagonal Triangles complete quadrangle and complete quadrilateral

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  • Chris Van Tienhoven
    Dear friends, Let P1, P2, P3, P4 be 4 coplanar points, no 3 of which are collinear and with no further restrictions. Let Oa be the Orthocenter of the diagonal
    Message 1 of 1 , Aug 27, 2012
      Dear friends,

      Let P1, P2, P3, P4 be 4 coplanar points, no 3 of which are collinear and with no further restrictions.
      Let Oa be the Orthocenter of the diagonal triangle of the complete quadrangle defined by points P1, P2, P3, P4.
      Let Ob be the Orthocenter of the diagonal triangle of the complete quadrilateral defined by the lines P1.P2, P2.P3, P3.P4, P4.P1.
      Let S be the diagonal crosspoint P1.P3 ^ P2.P4.
      Proof that Oa, Ob and S are collinear.

      Best regards,

      Chris van Tienhoven
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