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A pair of equal sides, and a pair of equal angles!

Source: Sharygin Correspondence Round 2024 P8

March 6, 2024
geometryquadrilateral

Problem Statement

Let ABCDABCD be a quadrilateral ∠B=∠D\angle B = \angle D and AD=CDAD = CD. The incircle of triangle ABCABC touches the sides BCBC and ABAB at points EE and FF respectively. Prove that the midpoints of segments AC,BD,AE,AC, BD, AE, and CFCF are concyclic.
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