Question

circle a is congruent to circle j. chords (overline{bc},overline{cf},overline{eg},overline{kl},overline{lo},) and (overline{mp}) are congruent. which arcs are congruent? check all that apply. (overset{\frown}{bc}congoverset{\frown}{mp}) (overset{\frown}{bc}congoverset{\frown}{mo}) (overset{\frown}{cf}congoverset{\frown}{kp}) (overset{\frown}{eg}congoverset{\frown}{kl}) (overset{\frown}{lo}congoverset{\frown}{mp})

Explanation:

Step1: Recall the property of congruent circles and chords

In congruent circles, congruent chords subtend congruent arcs.

Step2: Analyze each option

Given chords \(BC, CF, EG, KL, LO, MP\) are congruent.

• For \(\widehat{BC}\cong\widehat{MP}\), since \(BC\) and \(MP\) are congruent chords in congruent circles \(A\) and \(J\), the arcs they subtend are congruent.
• For \(\widehat{BC}\cong\widehat{LO}\), as \(BC\) and \(LO\) are congruent chords in congruent circles, the arcs are congruent.
• For \(\widehat{CF}\cong\widehat{KL}\), because \(CF\) and \(KL\) are congruent chords in congruent circles, the arcs are congruent.

Answer:

\(\widehat{BC}\cong\widehat{MP}\), \(\widehat{BC}\cong\widehat{LO}\), \(\widehat{CF}\cong\widehat{KL}\)