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Proving inequalities of areas given inequality of sides

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October 30, 2010
inequalitiesgeometrygeometry unsolved

Problem Statement

For two given triangles A1A2A3A_1A_2A_3 and B1B2B3B_1B_2B_3 with areas ΔA\Delta_A and ΔB\Delta_B, respectively, AiAk≥BiBk,i,k=1,2,3A_iA_k \ge B_iB_k, i, k = 1, 2, 3. Prove that ΔA≥ΔB\Delta_A \ge \Delta_B if the triangle A1A2A3A_1A_2A_3 is not obtuse-angled.
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