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bisector wanted, 30^o, 150^o, AB=BD (2020 Novosibirsk Oral Geo Oly 8.7)

Source:

May 20, 2021
geometryangle bisectorangles

Problem Statement

You are given a quadrilateral ABCDABCD. It is known that ∠BAC=30o\angle BAC = 30^o, ∠D=150o\angle D = 150^o and, in addition, AB=BDAB = BD. Prove that ACAC is the bisector of angle CC.
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