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Equal segments in a cyclic quadrilateral

Source: Greece JBMO TST 2023 P2

July 29, 2023
geometrycyclic quadrilateral

Problem Statement

Consider a cyclic quadrilateral ABCDABCD in which BC=CDBC = CD and AB<ADAB < AD. Let EE be a point on the side ADAD and FF a point on the line BCBC such that AE=AB=AFAE = AB = AF. Prove that EF∥BDEF \parallel BD.
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