Question 157
In triangle $ABC$, let $A'$, $B'$, $C'$ be the midpoints of $BC$, $AC$, $AB$ respectively. Let $B^*$, $C^*$ be points on $AC$, $AB$ such that $BB^*$, $CC^*$ are altitudes of triangle $ABC$. Let $B^\#$, $C^\#$ be the midpoints of $BB^*$, $CC^*$ respectively. Suppose $B'B^\#$ and $C'C^\#$ meet at $K$, and $AK$ meets $BC$ at $L$. Prove that $\angle BAL = \angle CAA'$.