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Comparing areas of two triangles with same circumcircle

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November 3, 2010
geometrycircumcircleincenterangle bisectorgeometry unsolved

Problem Statement

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?
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