Let-P-1-P-2-P-n-be-a-convex-polygon-with-the-following-property-for-any-two-vertices-P-i-and-P-j-there-exists-a-vertex-P-k-such-that-the-segment-P-i-P-j-is-seen-from-P-k-under-an-ang

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Question Number 16875 by Tinkutara last updated on 27/Jun/17

$$\mathrm{Let}{P}_1,P_2,\dots ,P_n\mathrm{be}\mathrm{a}\mathrm{convex}\mathrm{polygon}$$$$\mathrm{with}\mathrm{the}\mathrm{following}\mathrm{property}:\mathrm{for}\mathrm{any}$$$$\mathrm{two}\mathrm{vertices}{P}_i\mathrm{and}{P}_j,\mathrm{there}\mathrm{exists}\mathrm{a}$$$$\mathrm{vertex}{P}_k\mathrm{such}\mathrm{that}\mathrm{the}\mathrm{segment}{P}_i{P}_j$$$$\mathrm{is}\mathrm{seen}\mathrm{from}{P}_k\mathrm{under}\mathrm{an}\mathrm{angle}\mathrm{of}60°.$$$$\mathrm{Prove}\mathrm{that}\mathrm{the}\mathrm{polygon}\mathrm{is}\mathrm{an}$$$$\mathrm{equilateral}\mathrm{triangle}.$$

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