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2010 JBMO Shortlist G2

Source: 2010 JBMO Shortlist G2

October 8, 2017

geometryJBMO

Problem Statement

Consider a triangle

{ABC}

and let

{M}

be the midpoint of the side

{BC.}

Suppose

{\angle MAC=\angle ABC}

and

{\angle BAM=105^{\circ}.}

Find the measure of

{\angle ABC}