IMO 1978 LL CZS8

For two given triangles A1A2A3 and B1B2B3 with areas ∆A

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IMO 1978 LL CZS8

Origin: CZS

Problem

For two given triangles A1A2A3 and B1B2B3 with areas ∆A and ∆B, respectively, AiAk \geqBiBk, i, k = 1, 2, 3. Prove that ∆A \geq∆B if the triangle A1A2A3 is not obtuse-angled.