IMO Shortlist 1989 problem 1


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ABC is 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 A_0. Define B_0 and C_0 similarly. Prove that the area of triangle A_0B_0C_0 = 2 \cdot area of hexagon AC_1BA_1CB_1 \geq 4 \cdot area of triangle ABC.
Izvor: Međunarodna matematička olimpijada, shortlist 1989