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ASU 114 All Soviet Union MO 1968 rational sides and diagonals

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June 20, 2019
geometry

Problem Statement

Given a quadrangle ABCDABCD. The lengths of all its sides and diagonals are the rational numbers. Let OO be the point of its diagonals intersection. Prove that ∣AO∣|AO| - the length of the [AO][AO] segment is also rational.
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