HYACINTHOS 16741

• [Antreas P. Hatzipolakis]:

  Let ABC be a triangle, L a line passing through P and Q,
  and La,Lb,Lc the parallels to L through A,B,C, resp.
  
  Let Ma,Mb,Mc be the Reflections of BC,CA,AB, in
  La,Lb,Lc, resp.
  
  What can be said about the triangle bounded by the
  lines (Ma,Mb,Mc)?
  
  If Q is fixed point, which is the locus of P such that
  ABC, (MaMbMc) are perspective?
  
  If P'Q' is the PQ-line of (Ma,Mb,Mc) are the lines
  PQ, P'Q' parallels?
  (Definition: If P = (x:y:z) wrt triangle ABC, then
  P' = (x:y:z) wrt the triangle (Ma,Mb,Mc))
  
  What is the intersection point of PP' and QQ'?
  
  Special Cases:
  
  PQ = OH line (Euler Line) or OI line of ABC.
  
  
  APH