Question 49
Let the triangle $\triangle ABC$ be given. On the arc $\overset{\frown}{BC}$ of the circumcircle of $\triangle ABC$ which does not contain the point $A$, points $X$ and $Y$ are chosen such that $\angle BAX = \angle CAY$. Let $M$ be the midpoint of the chord $AX$. Prove that $\overline{BM} + \overline{CM} \gt \overline{AY}$.
