Question

which of the following segments is a diameter of ⊙o? a. $overline{ab}$ b. $overline{ac}$ c. $overline{od}$ d. $overline{db}$

Explanation:

Step1: Recall diameter definition

A diameter of a circle is a line - segment that passes through the center of the circle and has its endpoints on the circle.

Step2: Analyze each option

• Option A: $\overline{AB}$ does not pass through the center $O$, so it is not a diameter.
• Option B: $\overline{AC}$ passes through the center $O$ and has endpoints $A$ and $C$ on the circle, so it is a diameter.
• Option C: $\overline{OD}$ has one endpoint at the center $O$ and the other on the circle, it is a radius, not a diameter.
• Option D: $\overline{DB}$ does not pass through the center $O$, so it is not a diameter.

Answer:

B. $\overline{AC}$