HYACINTHOS 3130

• Antreas P. Hatzipolakis
  
  Let ABC be a triangle and La, Lb, Lc the prpendicular bisectors of BC, CA, AB,
  resp., and AA', BB', CC' the three altitudes of ABC.
  
  Let Ab = AA' /\ Lb
  Ac = AA' /\ Lc
  
  A1 = BAb /\ CAc
  
  A2 = BAc /\ CAb
  
  Similarly we define the points B1, C1; B2, C2.
  
  Are the triangles A1B1C1, A2B2C2 in perspective with ABC?
  (as I believe...)
  
  
  APH