HYACINTHOS 7892

• Dear friends,
  
  I don't know if the following properties are known.
  They are not mentionned in the ETC
  
  
  - 1 -
  
  Let A°B°C° be the cevian triangle of the incenter I of triangle ABC.
  Let Za be the centroid of the triangle AB°C°.
  Define Zb en Zc cyclically.
  X(37) is the perspector of the triangles ABC and ZaZbZc.
  
  - 2 -
  
  Let A°, B° and C° be the reflections of the incenter in the sides
  BC, CA and AB then AA°, BB° and CC° concur in X(79).
  
  - 3 -
  
  Let A°B°C° be the cevian triangle of the incenter I of triangle ABC.
  Let Ka be the Lemoine point of the triangle AB°C°.
  Define Kb en Kc cyclically.
  X(81) is the perspector of the triangles ABC and KaKbKc.
  
  - 4 -
  
  Let A°B°C° be the cevian triangle of the Gergonne point G of
  triangle ABC.
  Let A*B*C* be the cevian triangle of the Gergonne point G° of
  triangle A°B°C°
  X(173) is the perspector of the triangles ABC and A*B*C*.
  
  
  
  Greetings from Belgium
  
  
  Eric Danneels