Points $A_1,B_1,C_1$ are chosen on the sides $BC,CA,AB$ of a triangle $ABC$ respectively.The circumcircles of triangles $AB_1C_1,BC_1A_1,CA_1B_1$ intersect the circumcircle of triangle $ABC$ again at points $A_2,B_2,C_2$ respectively.($A_2 \neq A,B_2 \neq B,C_2 \neq C$).Points $A_3,B_3,C_3$ are symmetric to $A_1,B_1,C_1$ with respect to the midpoints of the sides $BC,CA,AB$ respectively.Prove that the triangles
$A_2B_2C_2$ and $A_3B_3C_3$ are similar.
IMO-2006-G9
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
বড় ভালবাসি তোমায়,মা
- Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.