Geometry · Parallelogram · Triangle inequality · Interior point · Perimeter

Problem 5, 1999

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RegionalProof

Let \(M\) be an interior point of a parallelogram \(ABCD\). Prove that

\[ MA + MB + MC + MD < \text{the perimeter of } ABCD . \]
A B C D M
The four distances to be bounded.

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Serbian Regional Competition (Okruzno takmicenje) 1999, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source