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min area of an hexagon, lines through O // sides ABC 2019 BMT Individual 16

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January 5, 2022
geometryareasarea of a trianglehexagongeometric inequality

Problem Statement

Let ABCABC be a triangle with AB=26AB = 26, BC=51BC = 51, and CA=73CA = 73, and let OO be an arbitrary point in the interior of △ABC\vartriangle ABC. Lines ℓ1\ell_1, ℓ2\ell_2, and ℓ3\ell_3 pass through OO and are parallel to AB‾\overline{AB}, BC‾\overline{BC}, and CA‾\overline{CA}, respectively. The intersections of ℓ1\ell_1, ℓ2\ell_2, and ℓ3\ell_3 and the sides of △ABC\vartriangle ABC form a hexagon whose area is AA. Compute the minimum value of AA.
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