Question 115
Let $ABC$ be a triangle and $\omega$ be its circumcircle. The point $M$ is the midpoint of arc $BC$ not containing $A$ on $\omega$ and $D$ is chosen so that $DM$ is tangent to $\omega$ and is on the same side of $AM$ as $C$. It is given that $AM = AC$ and $\angle DMC = 38^{\circ}$. Find the measure of angle $\angle ACB$.