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Question Number 16069 by Tinkutara last updated on 21/Jun/17

$$\mathrm{In}\mathrm{the}\mathrm{interior}\mathrm{of}\mathrm{a}\mathrm{quadrilateral}$$$$ABCD,\mathrm{consider}\mathrm{a}\mathrm{variable}\mathrm{point}P.$$$$\mathrm{Prove}\mathrm{that}\mathrm{if}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{distances}\mathrm{from}$$$$P\mathrm{to}\mathrm{the}\mathrm{sides}\mathrm{is}\mathrm{constant},\mathrm{then}ABCD$$$$\mathrm{is}\mathrm{a}\mathrm{parallelogram}.$$

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