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B, E, D, F concyclic if AB = AD, BE = EC - All-Russian MO 1999 Regional (R4) 9.2

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September 25, 2024
geometryConcyclic

Problem Statement

In triangle ABCABC, on side ACAC there are points DD and EE, that AB=ADAB = AD and BE=ECBE = EC (EE between AA and DD). Point FF is midpoint of arc BCBC of circumcircle of triangle ABCABC. Prove that the points B,E,D,FB, E, D, F lie on the same circle.
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