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MMO 300 Moscow MO 1955 AC - DA > 1, BC - BD > 1, EC - ED > 1

Source:

August 17, 2019
geometrygeometric inequality

Problem Statement

Inside △ABC\vartriangle ABC, there is fixed a point DD such that AC−DA>1AC - DA > 1 and BC−BD>1BC - BD > 1. Prove that EC−ED>1EC - ED > 1 for any point EE on segment ABAB.
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