Question

question 16 of 44 given ⊙o below, if $widehat{ab}$ and $widehat{bc}$ are congruent, what is the measure of chord $overline{bc}$?
diagram: circle with center o, points a, b, c on circumference. oa, ob, oc are radii. ab is labeled 14.5, angle ∠aob is 115°.
a. 7.5 units
b. 14.5 units
c. 12.5 units
d. 10.5 units

Explanation:

Step1: Recall congruent arcs and chords

In a circle, congruent arcs correspond to congruent chords. So if \(\widehat{AB}\) and \(\widehat{BC}\) are congruent, then chords \(AB\) and \(BC\) are congruent.

Step2: Identify length of \(AB\)

From the diagram, the length of chord \(AB\) is given as \(14.5\) units.

Step3: Determine length of \(BC\)

Since \(AB\cong BC\) (because \(\widehat{AB}\cong\widehat{BC}\)), the length of \(BC\) is equal to the length of \(AB\), which is \(14.5\) units.

Answer:

B. 14.5 units