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(IMO 1989-2) Area of $A_0B_0C_0$

Posted: Wed Feb 01, 2012 12:01 am
by Labib
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,
$S_{A_0B_0C_0}=2S_{AC_1BA_1CB_1}≥ 4S_{ABC}$.