Given a circle with center $L$, we are given that the length of the segment $RT$ is 19 meters. We are asked to find the length of segment $LW$. Since $L$ is the center of the circle, $LR$, $LW$, and $LT$ are radii of the circle.

1. Problem Description

Given a circle with center $L$, we are given that the length of the segment $RT$ is 19 meters. We are asked to find the length of segment $LW$.

Since $L$ is the center of the circle, $LR$, $LW$, and $LT$ are radii of the circle.

2. Solution Steps

Since $LR$ and $LT$ are radii of the circle, the length of $LR$ is the same as the length of $LT$. Therefore, $LR = LT$. Also, since $RT$ passes through the center $L$, it is the diameter of the circle.

Since the length of $RT$ is 19 meters, the length of the diameter of the circle is 19 meters. The radius of a circle is half the length of the diameter. Therefore, $LR = LT = LW = \frac{RT}{2} = \frac{19}{2} = 9.5$ meters.

3. Final Answer

9. 5