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Found problems: 1

1955 Moscow Mathematical Olympiad, 310
Tags: sidelengths of triangle , triangle , inequalities
Let the inequality $$Aa(Bb + Cc) + Bb(Aa + Cc) + Cc(Aa + Bb) > \frac{ABc^2 + BCa^2 + CAb^2}{2}$$ with given $a > 0, b > 0, c > 0$ hold for all $A > 0, B > 0, C > 0$. Is it possible to construct a triangle with sides of lengths $a, b, c$?