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MathNet 2012 Question 42

Math Olympiad Vault · MathNet 2012

Question 42

Triangle $ABC$ satisfies $\angle B \gt \angle C$. Let $M$ be the midpoint of $BC$, and let the perpendicular bisector of $BC$ meet the circumcircle of $\triangle ABC$ at a point $D$ such that points $A, D, C$, and $B$ appear on the circle in that order. Given that $\angle ADM = 68^{\circ}$ and $\angle DAC = 64^{\circ}$, find $\angle B$.