IMO 1972 LL CZS12

A circle k = (S, r) is given and a hexagon AA′BB′CC′ inscribed

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IMO 1972 LL CZS12

Origin: CZS

Problem

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