Question 49
Let $ABC$ be an acute isosceles triangle with orthocenter $H$. Let $M$ and $N$ be the midpoints of sides $\overline{AB}$ and $\overline{AC}$, respectively. The circumcircle of triangle $MHN$ intersects line $BC$ at two points $X$ and $Y$. Given $XY = AB = AC = 2$, compute $BC^2$.