Question

if the length of \\( \overline { a b } \\) is 13 millimeters, what is the length of \\( \overline { c d } \\)?
\\( \bigcirc \\) a \\( c d = ( 1 / 2 ) a b = 6.5 \mathrm { mm } \\)
\\( \bigcirc \\) b \\( c d = a b = 13 \mathrm { mm } \\)
\\( \bigcirc \\) c \\( c d = 2 a b = 26 \mathrm { mm } \\)

Explanation:

Step1: Recall the property of chords in a circle

In a circle, if two chords are equidistant from the center, then the chords are congruent.

Step2: Analyze the given figure

Here, chords \( AB \) and \( CD \) are equidistant from the center \( O \) (the perpendicular distances from \( O \) to \( AB \) and \( CD \) are equal as indicated by the marks).

Step3: Apply the property

Since \( AB \) and \( CD \) are equidistant from the center \( O \), by the chord - distance property of a circle, \( AB\cong CD \). Given \( AB = 13mm \), so \( CD=AB = 13mm \).

Answer:

B. \( CD = AB = 13mm \)