Question

if the length of \\(\overline{ab}\\) is 24 centimeters, what is the length of \\(\overline{cd}\\)?
enter the answer in the space provided. use numbers instead of words.
\\(\square\\) centimeters

Explanation:

Step1: Identify congruent central angles

From the diagram, $\angle AOB = \angle COD$ (they are vertical angles, marked as equal right angles).

Step2: Apply chord theorem

In a circle, if two central angles are congruent, their corresponding chords are congruent. Since $\angle AOB = \angle COD$, then $\overline{AB} = \overline{CD}$.

Step3: Substitute given length

Given $\overline{AB} = 24$ cm, so $\overline{CD} = 24$ cm.

Answer:

24 centimeters