In a $\mathrm{circle}$, if two $\mathrm{chords}$ are $\mathrm{congruent}$, what can be said about the $\mathrm{arcs}$ they subtend?

• A. The $\mathrm{arcs}$ subtended by the $\mathrm{congruent}$ $\mathrm{chords}$ are always different in length.
• B. The $\mathrm{arcs}$ subtended by the $\mathrm{congruent}$ $\mathrm{chords}$ are $\mathrm{congruent}$.
• C. The $\mathrm{arcs}$ subtended by the $\mathrm{congruent}$ $\mathrm{chords}$ are always $\mathrm{semicircles}$.
• D. The $\mathrm{arcs}$ subtended by the $\mathrm{congruent}$ $\mathrm{chords}$ are not necessarily $\mathrm{congruent}$.

Answer: (B)

Verified step by step guidance

1. Recall the definition of a chord in a circle: a chord is a line segment with both endpoints on the circle.
2. Understand that the arc subtended by a chord is the portion of the circle's circumference that lies between the endpoints of the chord.
3. Use the property that congruent chords in the same circle subtend congruent arcs. This means if two chords have the same length, the arcs they cut off on the circle are also equal in measure.
4. This property follows from the fact that equal chords are equidistant from the center of the circle, which implies the central angles subtending these chords are equal, and thus the arcs are congruent.
5. Therefore, the correct conclusion is that the arcs subtended by congruent chords are congruent.