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AD = DU if <CBA = 60^o, <CBU = 45^o, U circumcenter

Source: 2021 Austrian Mathematical Olympiad Junior Regional Competition , Problem 2

September 12, 2021
geometryequal segmentsCircumcenter

Problem Statement

A triangle ABCABC with circumcenter UU is given, so that ∠CBA=60o\angle CBA = 60^o and ∠CBU=45o\angle CBU = 45^o apply. The straight lines BUBU and ACAC intersect at point DD. Prove that AD=DUAD = DU.
(Karl Czakler)
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