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To determine which segment is the diameter of the circle, we need to find a line segment that passes through the center \( O \) of the circle and has endpoints on the circle itself.

In this diagram:
1. Segment \( \overline{OD} \) connects point \( O \) to point \( D \), but \( D \) is on the circle while \( O \) is the center, so it cannot be a diameter because it doesn't reach both ends of the circle.
2. Segment \( \overline{AC} \) connects two points on the circle but does not pass through the center \( O \), so it is not a diameter.
3. Segment \( \overline{DB} \) also connects two points on the circle but does not pass through the center, making it not a diameter.
4. Segment \( \overline{AB} \) connects two points on the circle and passes through the center \( O \), which makes it the diameter.

### Answer:
The correct answer is **D. \( \overline{AB} \)**.

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Here are some related questions:
1. What defines a diameter in a circle?
2. How do you calculate the length of a diameter if the radius is known?
3. What is the relationship between the diameter and the radius?
4. How can you identify the center of a circle given multiple chords?
5. What are the properties of a chord in relation to the circle's center?

**Tip:** The diameter is always the longest chord in a circle and is equal to twice the radius.

Which of the following segments is a diameter of circle O?

Learn how to identify the diameter of a circle in this geometry problem. Understand key concepts about circles, including diameter, chords, and center. Suitable for students in Grades 6-8.

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