1. **Problem:** Find the length of segment NM in a circle with center K and radius 16. Points L and N lie on the circumference, M is outside the circle. Line segment MN intersects the circle at L. Given: ML = $x - 3$, LN = $x + 3$. 2. **Formula and rules:** When a line segment passes through a circle intersecting it at two points, the segment inside the circle is the sum of the two parts on the chord. Here, $MN = ML + LN$. 3. **Work:** - Given $ML = x - 3$ and $LN = x + 3$. - So, $MN = (x - 3) + (x + 3) = 2x$. 4. **Additional information:** Since L and N are on the circle and K is the center with radius 16, the chord LN length can be found if needed, but the problem only asks for NM. 5. **Conclusion:** The length of $NM$ is $2x$. Since the problem does not provide a value for $x$, the answer is expressed in terms of $x$. **Final answer:** $$NM = 2x$$