1970 Canadian MO Problems/Problem 5

Problem

A quadrilateral has one vertex on each side of a square of side-length 1. Show that the lengths $a$ , $b$ , $c$ and $d$ of the sides of the quadrilateral satisfy the inequalities $2\le a^2+b^2+c^2+d^2\le 4.$

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1970 Canadian MO Problems/Problem 5

Problem

Solution