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Question Number 16737 by Tinkutara last updated on 26/Jun/17

$$\mathrm{A}\mathrm{convex}\mathrm{hexagon}\mathrm{is}\mathrm{given}\mathrm{in}\mathrm{which}$$$$\mathrm{any}\mathrm{two}\mathrm{opposite}\mathrm{sides}\mathrm{have}\mathrm{the}$$$$\mathrm{following}\mathrm{property}:\mathrm{the}\mathrm{distance}$$$$\mathrm{between}\mathrm{their}\mathrm{midpoints}\mathrm{is}\frac{\sqrt{3}}{2}\mathrm{times}\mathrm{the}$$$$\mathrm{sum}\mathrm{of}\mathrm{their}\mathrm{lengths}.\mathrm{Prove}\mathrm{that}\mathrm{the}$$$$\mathrm{hexagon}\mathrm{is}\mathrm{equiangular}.$$

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