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9155Reflections

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  • xpolakis
    Jan 30, 2004
      Let ABC be a triangle, P a point, and Oa;Ha, Ob;Hb, Oc;Hc,
      the circumcenters, Orthocenters of PBC, PCA, PAB.

      The locus of P such that the lines
      OaHa, ObHb, OcHc [Euler Lines] are concurrent is well-known.

      Now, let O'a, H'a be the reflections of Oa, Ha in BC, resp.
      Similarly O'b, H'b; O'c,H'c.

      Which is the locus of P such that the lines

      1. O'aHa, O'bHb, O'cHc

      2. OaH'a, ObH'b, OcH'c

      are concurrent?


      Greetings from Athens

      Antreas
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