HYACINTHOS 7689

• Dear Clark Kimberling and all Hyacinthians,
  
  In the ETC entry related to the point X(65), you
  write that X(65) is the perspector of triangle ABC
  and the Yff central triangle.
  
  I believe this is not true. X(65) is the
  perspector of triangle ABC and the extangents
  triangle; hence, the perspector of triangle ABC
  and the Yff central triangle is
  X(65)-of-the-Yff-central-triangle. [In fact,
  triangle ABC is the extangents triangle of the
  Yff central triangle.]
  
  This point is X(177) of triangle ABC, the
  so-called FIRST MID-ARC POINT. This is confirmed
  by calculations and drawing.
  
  I have used the fact that the trilinears of the
  A-vertex of the Yff central triangle are
  
  ( cos(B/2) cos(C/2)
  : cos(C/2)(cos(C/2) + cos(A/2))
  : cos(B/2)(cos(A/2) + cos(B/2)) ).
  
  [These are from the TCCT, but corrected.]
  
  Sincerely,
  Darij Grinberg