MathNet 2012 Question 72

Let $ABC$ be an acute-angled triangle with circumcircle $\Gamma$, and let $O, H$ be the triangle's circumcenter and orthocenter respectively. Let also $A'$ be the point where the angle bisector of angle $BAC$ meets $\Gamma$. If $A'H = AH$, find the measure of angle $BAC$.


Figure 4: Exercise G4.