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A brilliant geo problem

Source:

July 22, 2019
geometry

Problem Statement

Acute triangle ABCABC has ∠BAC<45∘\angle BAC < 45^\circ. Point DD lies in the interior of triangle ABCABC so that BD=CDBD = CD and ∠BDC=4∠BAC\angle BDC = 4 \angle BAC. Point EE is the reflection of CC across line ABAB, and point FF is the reflection of BB across line ACAC. Prove that lines ADAD and EFEF are perpendicular.
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