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RU-ALLRUSSIAN 1969 Problem 1

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In the quadrilateral ABCD, BC is parallel to AD. The point E lies on the segment AD and the perimeters of ABE, BCE and CDE are equal. Prove that BC=AD/2\mathrm{BC} = \mathrm{AD} / 2 .

Dataset text NuminaMath olympiads. Quoted with source.

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BC = AD / 2

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