Question

which of the following best describes the relationship between the chords (overline{nr}) and (overline{qs}) shown in the diagram below? (\bigcirc) a. they are parallel. (\bigcirc) b. they are perpendicular. (\bigcirc) c. they are not congruent. (\bigcirc) d. they are congruent.

Explanation:

In a circle, if two chords are equidistant from the center, they are congruent. Here, the distance from the center \( V \) to chord \( \overline{NR} \) (segment \( VT \)) and to chord \( \overline{QS} \) (segment \( VU \)) is both \( 6.7 \), so the chords are equidistant from the center. By the theorem, equidistant chords from the center are congruent. Also, the chords are not necessarily parallel (no indication of parallel lines) or perpendicular (the right angles are with the perpendicular from the center, not between the chords). Option C is wrong as they are congruent.

Answer:

D. They are congruent.