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JBMO Shortlist 2019 G3

Source:

September 12, 2020
geometry

Problem Statement

Let ABCABC be a triangle with incenter II. The points DD and EE lie on the segments CACA and BCBC respectively, such that CD=CECD = CE. Let FF be a point on the segment CDCD. Prove that the quadrilateral ABEFABEF is circumscribable if and only if the quadrilateral DIEFDIEF is cyclic.
Proposed by Dorlir Ahmeti, Albania
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