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<ADB+<BEC+<CFA=? BA=BC, AD=AC, BE=BA , CF=CB (2023 Novosibirsk Oral Geo Oly 7.6)

Source:

September 4, 2023
geometryequal segmentsanglesisosceles

Problem Statement

An isosceles triangle ABCABC with base ACAC is given. On the rays CACA, ABAB and BCBC, the points D,ED, E and FF were marked, respectively, in such a way that AD=ACAD = AC, BE=BABE = BA and CF=CBCF = CB. Find the sum of the angles ∠ADB\angle ADB, ∠BEC\angle BEC and ∠CFA\angle CFA.
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