1. **Stating the problem:** We have points $l$, $m$, and $n$ on a circle with center $O$. The angle $\angle N M$ (interpreted as $\angle N M O$ or $\angle N M L$ depending on context) is given as $a$. We want to find relationships involving these points and angles. 2. **Understanding the problem:** Since $l$, $m$, and $n$ lie on a circle, angles subtended by the same chord or arcs have special properties. The center $O$ is the center of the circle. 3. **Key formulas and rules:** - The angle subtended by an arc at the center is twice the angle subtended at the circumference. - Angles in the same segment are equal. 4. **Applying the rule:** If $\angle N M$ is $a$ at the circumference, then the angle subtended by the same arc $N L$ at the center $O$ is $2a$. 5. **Conclusion:** Therefore, the central angle $\angle N O L = 2a$. This is a fundamental property of circle geometry relating central and inscribed angles.