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Construct M such that the sum is maximal

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August 29, 2010
geometry proposedgeometry

Problem Statement

Let A1A2A3A4A5A6A_1A_2A_3A_4A_5A_6 be a hexagon inscribed into a circle with center OO. Consider the circular arc with endpoints A1,A6A_1,A_6 not containing A2A_2. For any point MM of that arc denote by hih_i the distance from MM to the line AiAi+1 (1≤i≤5)A_iA_{i+1} \ (1 \leq i \leq 5). Construct MM such that the sum h1+⋯+h5h_1 + \cdots + h_5 is maximal.
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