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AD + DC>= AB if CD = BC = BE and ABCD is convex with E =AC\cap BD

Source: 2023 IGO Elementary P4

January 18, 2024
geometrygeometric inequality

Problem Statement

Let ABCDABCD be a convex quadrilateral. Let EE be the intersection of its diagonals. Suppose that CD=BC=BECD = BC = BE. Prove that AD+DC≥ABAD + DC\ge AB.
Proposed by Dominik Burek - Poland
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