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Cyclic quadrilateral with equal sides and unusual length condition

Source: 2nd Memorial Mathematical Competition "Aleksandar Blazhevski - Cane" - Problem 1

January 12, 2021
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral such that AB=ADAB=AD. Let EE and FF be points on the sides BCBC and CDCD, respectively, such that BE+DF=EFBE+DF=EF. Prove that ∠BAD=2∠EAF\angle BAD = 2 \angle EAF.
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