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21878X(5430) = CENTER OF THE GRIGORIEV CONIC

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  • Hyacinthos-owner@yahoogroups.com
    Apr 1, 2013
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      <q>Let L_A be the line parallel to line BC and tangent to the
      circumcircle of triangle ABC and define L_B and L_C cyclically. </q>

      Let L_A be the parallel to BC tangent to circumcircle on the
      positive side of BC, and M_A the parallel to BC tangent to
      circumcircle on the negative side of BC.
      Similarly L_B, M_B, L_C, M_C.
      Let A'B'C', A"B"C" be the triangles bounded by the lines
      (L_A,L_B,L_C) and (M_A,M_B,M_C).

      By similar constructions as described in the point's entry,
      do we get eight conics?

      That is, conics respective to A'B'C', A"B"C", A'B"C", A"B'C",
      A"B"C', A"B'C', A'B"C', A'B'C" ?

      Or just only two, respective to A'B'C', A"B"C", whose the centers
      are symmetric with center of symmetry O?

      APH