Question 47
Let $I$ be the incenter of triangle $ABC$. $X$ is a point on arc $BC$ of the circumcircle of triangle $ABC$ such that if $E$ and $F$ are the feet of the perpendiculars from $X$ to $BI$ and $CI$, respectively, and $M$ is the midpoint of $EF$, then $MB = MC$. If $D$ is the foot of the perpendicular from $I$ to $BC$, show that $\angle BAD = \angle CAX$.