Question

if the length of \\(\overline{ab}\\) is 13 millimeters, what is the length of \\(\overline{cd}\\)?
enter the answer in the space provided. use numbers instead of words.
\\(\square\\) millimeters

Explanation:

Step1: Recall circle chord theorem

In a circle, if two chords are equidistant from the center, the chords are congruent (equal in length). The diagram shows that chords $\overline{AB}$ and $\overline{CD}$ are both equidistant from the center $O$.

Step2: Apply congruence to find length

Since $\overline{AB} = 13$ millimeters and $\overline{AB} \cong \overline{CD}$, the length of $\overline{CD}$ equals the length of $\overline{AB}$.
$CD = AB = 13$

Answer:

13 millimeters