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Isosceles triangle and strange point and angle

Source: Latvian TST 2021 Day 1 P3

March 12, 2021
geometry

Problem Statement

Given isosceles △ABC\triangle ABC with AB=ACAB = AC and ∠BAC=22∘\angle BAC = 22^{\circ}. On the side BCBC point DD is chosen such that BD=2CDBD = 2CD. The foots of perpendiculars from BB to lines ADAD and ACAC are points EE, FF respectively. Find with the proof value of the angle ∠CEF\angle CEF.
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