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Coaxial Circles

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  • Antreas
    Let ABC be a triangle, L a line and La, Lb, Lc its reflections in BC,CA,AB, resp. Denote A B C the triangle bounded by the lines L1,L2,L3. There was a
    Message 1 of 2 , Jan 2, 2012
      Let ABC be a triangle, L a line and La, Lb, Lc its reflections in
      BC,CA,AB, resp. Denote A'B'C' the triangle bounded by
      the lines L1,L2,L3.

      There was a discussion here about properties
      of the triangle A'B'C'. See message
      16734<http://tech.groups.yahoo.com/group/Hyacinthos/message/16734>

      Here is another one:

      Let HaHbHc be the orthic triangle.
      The circles (A'AHa), (B'BHb), (C'CHc)
      are coaxial.

      aph

      --
      http://anopolis72000.blogspot.com/2012/01/2o.html
    • Antreas Hatzipolakis
      Let ABC be a triangle, L a line and P, Q two points. The L intersects BC, CA, AB at A , B , C , resp. and AQ, BQ, CQ at A ,B , C , resp. The circumcircles of
      Message 2 of 2 , Mar 14 9:11 AM
        Let ABC be a triangle, L a line and P, Q two points.

        The L intersects BC, CA, AB at A', B', C', resp. and AQ, BQ, CQ at A",B", C", resp.

        The circumcircles of PA'A", PB'B", PC'C" are coaxial.

        Special Cases:

        Let L be passing through O, intersecting BC, CA, AB at A', B', C', resp. and AH, BH, CH at A", B", C", resp.
        The locus of the 2nd intersection of the circumcircles of HA'A", HB'B", HC'C", as L moves around O, is the circumcircle of ABC.

        Which is the locus of the 2nd intersection of the circumcircles of NA'A", NB'B", NC'C",  as L moves around O?
        In general, if P is a fixed point, the locus of the 2nd intersection of the circumcircles of PA'A", PB'B", PC'C", as L moves around O, is a conic?

        APH


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