Question

which of the following segments is a diameter of \\(\odot o\\)?

a. \\(\overline{db}\\)
b. \\(\overline{ab}\\)
c. \\(\overline{ac}\\)
d. \\(\overline{od}\\)

Explanation:

Define diameter of a circle

A diameter is a straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

Identify the center and points on the circle

The center of the circle is point \(O\).
The points on the circle are \(A\), \(B\), \(C\), \(D\), and \(E\).

Evaluate the given options

• \(\overline{DB}\): Endpoints \(D\) and \(B\) are on the circle, but the segment does not pass through the center \(O\).
• \(\overline{AB}\): Endpoints \(A\) and \(B\) are on the circle, and the segment passes directly through the center \(O\).
• \(\overline{AC}\): Endpoints \(A\) and \(C\) are on the circle, but the segment does not pass through the center \(O\).
• \(\overline{OD}\): One endpoint is the center \(O\) and the other is on the circle \(D\), which makes it a radius, not a diameter.

Answer:

• A. \(\overline{DB}\)
• B. \(\overline{AB}\) (Correct answer)
• C. \(\overline{AC}\)
• D. \(\overline{OD}\)