Question

question 3 of 10
fill in the blank. given \\(\odot o\\) below, you can conclude that \\(\overline{df}\\) is congruent to
\\(\underline{quadquad}\\).
a. \\(\overline{de}\\)
b. \\(\odot o\\)
c. \\(\overline{ac}\\)
d. \\(\overline{bc}\\)

Explanation:

Step1: Recall circle chord theorem

In a circle, if two perpendicular segments from the center to chords are congruent, then the chords are congruent.

Step2: Identify congruent segments

We see $OE = OA = 3.09$, with $OE \perp \overline{DF}$ and $OA \perp \overline{BC}$.

Step3: Apply theorem to find congruent chord

Since the distances from center $O$ to $\overline{DF}$ and $\overline{BC}$ are equal, $\overline{DF} \cong \overline{BC}$.

Answer:

D. $\overline{BC}$