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IMO ShortList 2002, geometry problem 2

Source: IMO ShortList 2002, geometry problem 2

September 28, 2004
geometryhomothetyinequalitiesgeometric inequalityTriangleIMO Shortlist

Problem Statement

Let ABCABC be a triangle for which there exists an interior point FF such that ∠AFB=∠BFC=∠CFA\angle AFB=\angle BFC=\angle CFA. Let the lines BFBF and CFCF meet the sides ACAC and ABAB at DD and EE respectively. Prove that AB+AC≥4DE. AB+AC\geq4DE.
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