Cannot solve this circle theorem problem any hints?

Question

I need to find out the angle S, tried lots of stuff, still couldn't solve it. Any hints?

Answer 1

$m\,\overset{\mmlToken{mo}{⏜}}{CD\,}=74^\circ$ because it is subtended by $\angle CBD$ which has a measure of $37^\circ$. Since $\overline{BD}$ is a diameter, $m\,\overset{\mmlToken{mo}{⏜}}{BC\,}=106^\circ$. Therefore, $m\angle BAC=53^\circ$.

Answer 2

Hint: call the top corner of the triangle $A$ and add the segment $OA$. That way you get an isocsceles triangle and you know one of its angles. That way you can find all the angles of this triangle. Do you see what is the relation between these angles and $S$?

Answer 3

Try running a radius to the point near the top of the circle. This gives you an isosceles triangle. Can you see where to go from there?