Question

question 10 of 10
fill in the blank. given ( odot o ) below, you can conclude that ( overline{so} ) is congruent to
________
a. ( odot o )
b. ( overline{wa} )
c. ( overline{wr} )
d. ( overline{ao} )

Explanation:

Step1: Recall the property of congruent segments

In a circle, if two segments are radii or if they are the distances from the center to chords of equal length (by the perpendicular - from - the - center - to - a - chord theorem: if two chords in a circle are congruent, then the distances from the center of the circle to the chords are congruent). Here, \( \overline{WR}\) and \( \overline{BI}\) are chords of length \(3.71\). The segments \( \overline{OA}\) and \( \overline{OS}\) are the distances from the center \(O\) to the chords \( \overline{WR}\) and \( \overline{BI}\) respectively.
Since the chords \( \overline{WR}\) and \( \overline{BI}\) are of equal length, by the perpendicular - from - the - center - to - a - chord theorem, the distances from the center to these chords are equal.

Answer:

D. \(\overline{AO}\)