Question

determining congruent arcs
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.
$square$ $overset{\frown}{bc} cong overset{\frown}{mp}$
$square$ $overset{\frown}{bc} cong overset{\frown}{mo}$
$square$ $overset{\frown}{cf} cong overset{\frown}{kp}$
$square$ $overset{\frown}{eg} cong overset{\frown}{kl}$
$square$ $overset{\frown}{lo} cong overset{\frown}{mp}$

Explanation:

Step1: Recall chord-arc congruence rule

In congruent circles, congruent chords correspond to congruent arcs.

Step2: Match congruent chords to arcs

Given congruent chords: $\overline{BC} \cong \overline{CF} \cong \overline{EG} \cong \overline{KL} \cong \overline{LO} \cong \overline{MP}$.

• $\overline{BC} \cong \overline{MP}$ → $\overset{\frown}{BC} \cong \overset{\frown}{MP}$
• $\overline{CF} \cong \overline{KL}$ (not an option), but $\overline{LO} \cong \overline{MP}$ → $\overset{\frown}{LO} \cong \overline{MP}$
• $\overline{EG} \cong \overline{KL}$ → $\overset{\frown}{EG} \cong \overset{\frown}{KL}$

Step3: Eliminate incorrect options

• $\overline{BC}

ot\cong \overline{MO}$ (MO is not a listed congruent chord) → $\overset{\frown}{BC}
ot\cong \overset{\frown}{MO}$

• $\overline{CF}

ot\cong \overline{KP}$ (KP is not a listed congruent chord) → $\overset{\frown}{CF}
ot\cong \overset{\frown}{KP}$

Answer:

$\overset{\frown}{BC} \cong \overset{\frown}{MP}$, $\overset{\frown}{EG} \cong \overset{\frown}{KL}$, $\overset{\frown}{LO} \cong \overset{\frown}{MP}$