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Find < BAC given MB = OI

Source: Baltic Way 2017 Problem 13

November 11, 2017
geometryincentercircumcircle

Problem Statement

Let ABCABC be a triangle in which ∠ABC=60∘\angle ABC = 60^{\circ}. Let II and OO be the incentre and circumcentre of ABCABC, respectively. Let MM be the midpoint of the arc BCBC of the circumcircle of ABCABC, which does not contain the point AA. Determine ∠BAC\angle BAC given that MB=OIMB = OI.
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