IMO Shortlist 1989 problem 6


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For a triangle ABC, let k be its circumcircle with radius r. The bisectors of the inner angles A, B, and C of the triangle intersect respectively the circle k again at points A', B', and C'. Prove the inequality

16Q^3 \geq 27 r^4 P,

where Q and P are the areas of the triangles A'B'C' and ABC respectively.
Izvor: Međunarodna matematička olimpijada, shortlist 1989