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Anything but geometry

Source: Baltic Way 2004 Problem 17

November 19, 2004
geometryrectangleinequalitiesgeometry proposed

Problem Statement

Consider a rectangle with sidelengths 3 and 4, pick an arbitrary inner point on each side of this rectangle. Let x,y,zx, y, z and uu denote the side lengths of the quadrilateral spanned by these four points. Prove that 25≤x2+y2+z2+u2≤5025 \leq x^2+y^2+z^2+u^2 \leq 50.
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