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<ACB = 3 <DCB , if <CAB = 2 <ABC, AD = BD, CD = AC

Source: Switzerland - Swiss ΜΟ 2019 p7

July 14, 2020
geometryequal anglesequal segmentsangles

Problem Statement

Let ABCABC be a triangle with ∠CAB=2∠ABC\angle CAB = 2 \angle ABC. Assume that a point DD is inside the triangle ABCABC exists such that AD=BDAD = BD and CD=ACCD = AC. Show that ∠ACB=3∠DCB\angle ACB = 3 \angle DCB.
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