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RU-SPB 2011 Problem 95

    ABCDABCD - convex quadrilateral. ∠A+∠D=150,∠B<150,∠C<150\angle A+ \angle D=150, \angle B<150, \angle C<150 Prove, that area ABCDABCD is greater than 14(AB∗CD+AB∗BC+BC∗CD)\frac{1}{4}(AB*CD+AB*BC+BC*CD)

    Dataset text AI-MO AoPS. Quoted with source.

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