(IMO 1989-2) Area of $A_0B_0C_0$

Discussion on International Mathematical Olympiad (IMO)
User avatar
Joined:Thu Dec 09, 2010 10:58 pm
Location:Dhaka, Bangladesh.
(IMO 1989-2) Area of $A_0B_0C_0$

Unread post by Labib » Wed Feb 01, 2012 12:01 am

Let $ABC$ be a triangle. The bisector of $\angle A$ meets the circumcircle
of triangle $ABC$ in $A_1$. Points $B_1$ and $C_1$ are defined similarly. Let $AA_1$
meet the lines that bisect the two external angles at $B$ and $C$ in point $A_0$.
Define $B_0$ and $C_0$ similarly. If $S_{X_1X_2...X_n}$ denotes the area of the polygon
$X_1 X_2 . . . X_n$ , prove that,
$S_{A_0B_0C_0}=2S_{AC_1BA_1CB_1}≥ 4S_{ABC}$.
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.

"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

Post Reply