IrMO 1989 Problem 1

A quadrilateral $ABCD$ is inscribed, as shown, in a square of area one unit. Prove that $2\le |AB|^2+|BC|^2+|CD|^2+|DA|^2\le 4$

D

A

B

C

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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