Let $\overline{PQ}$, $\overline{RS}$, and $\overline{TU}$ be parallel chords of a circle. The distance between chords $\overline{PQ}$ and $\overline{RS}$ is 4, and the distance between chords $\overline{RS}$ and $\overline{TU}$ is also 4. If $PQ = 78$ and $TU = 50$, then find $RS$.
To find the length of chord $\overline{RS}$, we can use the property that the distance between two parallel chords in a circle is equal to the difference of their lengths.
We are given that the distance between $\overline{PQ}$ and $\overline{RS}$ is 4, so we can write this as an equation:
$\overline{PQ}$ - $\overline{RS}$ = 4
Substituting the given values, we have:
78 - $\overline{RS}$ = 4
Now, we can solve for $\overline{RS}$:
$\overline{RS}$ = 78 - 4
$\overline{RS}$ = 74
Therefore, the length of chord $\overline{RS}$ is 74.