Question

question 6 (5 points)
if the length of \\( \overline { a b } \\) is 24 centimeters,
what is the length of \\( \overline { c d } \\)?
\\( \bigcirc \\) a 24 cm
\\( \bigcirc \\) b 67 cm
\\( \bigcirc \\) c 12 cm

Explanation:

Step1: Recall the property of arcs in a circle

In a circle, if the central angles are equal, then the arcs are equal.

Step2: Analyze the central angles

The central angles for arc \(AB\) and arc \(CD\) are equal (assuming the un - labeled angles are equal as per the circle's symmetry in the given figure).

Step3: Use the arc - length property

Since the central angles for \(\overset{\frown}{AB}\) and \(\overset{\frown}{CD}\) are equal, the lengths of \(\overset{\frown}{AB}\) and \(\overset{\frown}{CD}\) are equal. Given \(l(\overset{\frown}{AB}) = 24\) cm, so \(l(\overset{\frown}{CD})=24\) cm.

Answer:

A. 24 cm