Question 35
Consider triangle $A B C$ such that $A B \leq A C$. Point $D$ on the arc $B C$ of the circumcircle of $A B C$ not containing point $A$ and point $E$ on side $B C$ are such that
$$
\measuredangle B A D=\measuredangle C A E\lt \frac{1}{2} \measuredangle B A C .
$$
Let $S$ be the midpoint of segment $A D$. If $\measuredangle A D E=\measuredangle A B C-\measuredangle A C B$ prove that
$$
\measuredangle B S C=2 \measuredangle B A C
$$
$$
\measuredangle B A D=\measuredangle C A E\lt \frac{1}{2} \measuredangle B A C .
$$
Let $S$ be the midpoint of segment $A D$. If $\measuredangle A D E=\measuredangle A B C-\measuredangle A C B$ prove that
$$
\measuredangle B S C=2 \measuredangle B A C
$$