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AX = AD if <BAX=<CDA,<ABC = <BCD, 2AB = CD (2016 Kyiv City MO 8.5.1)

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September 5, 2020
geometryequal anglesequal segments

Problem Statement

In the quadrilateral ABCDABCD, shown in fig. , the equations are true: ∠ABC=∠BCD\angle ABC = \angle BCD and 2AB=CD2AB = CD. On the side BCBC, a point XX is selected such that ∠BAX=∠CDA\angle BAX = \angle CDA. Prove that AX=ADAX = AD. https://cdn.artofproblemsolving.com/attachments/2/9/0884eb311d1e40300c1e5980fd53eaadfa7a25.png
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