31. A circle inscribed in an angle with vertex $O$ touches its sides at points $A$ and $B$. Ray $O X$ intersects this circle at two points $C$ and $D$ such that $O C=C D=1$. If $M$ is the point of intersection of ray $O X$ and segment $A B$, then what is the length of segment $O M$?
92.31. Answer. 4/3. Hint: Prove that $|O D||C M|=$ $=|O C||M D|$.