In-the-interior-of-a-quadrilateral-ABCD-consider-a-variable-point-P-Prove-that-if-the-sum-of-distances-from-P-to-the-sides-is-constant-then-ABCD-is-a-parallelogram-

Tinku Tara June 4, 2023 Geometry 0 Comments

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

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

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

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In-the-interior-of-a-quadrilateral-ABCD-consider-a-variable-point-P-Prove-that-if-the-sum-of-distances-from-P-to-the-sides-is-constant-then-ABCD-is-a-parallelogram-

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