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<ACB=90^o if AD = BD , <ACD = 3 <BAC, AM=//MD, CM//AB,

Source: 2021 JBMO TST Bosnia and Herzegovina P3

October 7, 2022
geometryright angleequal angles

Problem Statement

In the convex quadrilateral ABCDABCD, AD=BDAD = BD and ∠ACD=3∠BAC\angle ACD = 3 \angle BAC. Let MM be the midpoint of side ADAD. If the lines CMCM and ABAB are parallel, prove that the angle ∠ACB\angle ACB is right.
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