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Geometry about the right triangle from the right person

Source: Kyiv City MO 2022 Round 2, Problem 8.4

January 30, 2022
geometry

Problem Statement

Points D,E,FD, E, F are selected on sides BC,CA,ABBC, CA, AB correspondingly of triangle ABCABC with ∠C=90∘\angle C = 90^\circ such that ∠DAB=∠CBE\angle DAB = \angle CBE and ∠BEC=∠AEF\angle BEC = \angle AEF. Show that DB=DFDB = DF.
(Proposed by Mykhailo Shtandenko)
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