To determine the length of \( \overline{AB} \), we need to know the relationship between the segments and the midpoint \( C \). However, based on the provided options (13, 24, 17, 26), it seems like we must apply some reasoning or assumptions.
Since \( C \) is the midpoint of both \( \overline{AB} \) and \( \overline{DE} \), we can set up an equation based on the lengths:
If \( AB \) is of length \( x \), then the length of each half (from \( A \) to \( C \) and from \( C \) to \( B \)) will be \( \frac{x}{2} \).
Similarly, if \( DE \) is of length \( y \), then:
\[ C = \frac{y}{2} \text{ (for } DE\text{)} \]
Given that both segments share the same midpoint \( C \), their lengths must also relate to each other. However, since we don’t have any specific numerical relationships or additional details about \( DE \), we'll need to rely on the provided options.
Typically, the options suggest choosing a length that could reasonably represent \( x \).
We cannot definitively calculate the length without additional information, but we can select a plausible length from the provided options.
The generally accepted lengths are whole numbers likely to be measured directly. Taking into account the typical sizes for line segments in such problems, we might choose 24, as it is a common reasonable length used in examples like this.
Thus, a suspected reasonable answer is:
24.