Let $ABC$ be an acute triangle with $AB<AC$. Let $M$ be the midpoint of $BC$ and $E$ be the foot of altitude from $B$ to $AC$. The point $C'$ is the reflection of $C$ across $AM$. The point $D$ not equal to $C$ is placed on line $BC$ such that $AD=AC$. Prove that $B$ is the incenter of triangle $DEC'$.
