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22170Re: Envelopes

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  • Antreas Hatzipolakis
    Apr 22, 2014

      The problem was posed by the friend Dao Thanh Oai, in my wording:
      Let ABC be a triangle and L1,L2,L3 three parallel lines through A,B,C, resp. and let A'B'C' be the triangle bounded by the reflections of L1,L2,L3, in BC,CA,AB, resp.
      As the lines L1,L2,L3 move around A,B,C, the Euler line of the triangle
      A'B'C' passes through a fixed point.

       Let (Oa),(Na) be the circumcenter, NPC center of the triangle A'B'C', resp.
      Is the radical axis of (Oa), (Na) passing through a fixed point as well?
      And which is it?


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