Geometry · Parallelogram · Triangle inequality · Interior point · Perimeter
Let \(M\) be an interior point of a parallelogram \(ABCD\). Prove that
\[ MA + MB + MC + MD < \text{the perimeter of } ABCD . \]
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 1999, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source