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9967New property of X(1358) + a new related point

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  • Eric Danneels
    Jul 1, 2004
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      Dear Hyacinthians,

      X(1358) is defined in the current ETC as the Brisse-transform
      of X(101).

      I would like to present a new remarkable property of this point

      Let A'B'C' be the medial triangle of triangle ABC.
      Consider the circle, different from the ninepointcircle, through B'
      and C' touching the incircle. Let A* be the point where both circles
      touch. Define B* and C* similarly.

      X(1358) is the perspector of the triangles ABC and A*B*C*
      Its barycentrics are ( (b-c)^2/(b+c-a) : cyclic.....)

      If we replace the medial triangle by the orthic triangle we get a
      new point S with similar barycentrics

      S = ( (b-c)^2.(b+c-a)^3 : cyclic.....)

      Greetings from Bruges

      Eric Danneels
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