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ILL 1972 Problem 12

    A circle k=(S,r)k = (S, r) is given and a hexagon AA′BB′CC′AA'BB'CC' inscribed in it. The lengths of sides of the hexagon satisfy AA′=A′B,BB′=B′C,CC′=C′AAA' = A'B, BB' = B'C, CC' = C'A . Prove that the area PP of triangle ABCABC is not greater than the area P′P' of triangle A′B′C′A'B'C' . When does P=P′P = P' hold?

    Dataset text AI-MO AoPS. Quoted with source.

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