Question

question 9 of 10
fill in the blank. given ( odot o ) below, you can conclude that ( overline{xz} ) is congruent to

a. ( odot o )
b. ( overline{ac} )
c. ( overline{bc} )
d. ( overline{xy} )

Explanation:

Step1: Recall the chord - distance theorem

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

Step2: Analyze the given information

We are given that the distance from the center \(O\) to chord \(\overline{AC}\) (the length of the perpendicular segment from \(O\) to \(\overline{AC}\)) is \(2.2\), and the distance from the center \(O\) to chord \(\overline{XZ}\) (the length of the perpendicular segment from \(O\) to \(\overline{XZ}\)) is also \(2.2\).

Answer:

B. \(\overline{AC}\)