1.44. In a circle with center $O$, a chord $A B$ is drawn, intersecting the diameter at point $M$ and forming an angle of $60^{\circ}$ with the diameter. Find $O M$, if $A M=10$ cm, and $B M=4$ cm.
1.44. Draw $O P \perp A B$ (Fig. 1.36). Then $A P=B P=7$ cm and, therefore, $M P=3$ cm. Since $\angle P M O=60^{\circ}$, then $\angle M O P=30^{\circ}$ and $O M=2 M P=6 \text{ cm}$.

Answer: 6 cm.