Geometry · Square · Locus · Perpendicular bisector · Triangle inequality · Symmetry
Find all points \(X\) inside the square \(ABCD\) for which
\[ AX + CX = BX + DX . \]
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Serbian Regional Competition (Okruzno takmicenje) 2020, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source