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The problem involves identifying segments that are of the same length as \( AB \) in a geometric figure created with a straightedge and compass.

### Analysis:
1. The circles are centered at \( A \), \( B \), and \( C \), and were likely constructed with radii equal to other key segments.
2. The segment \( AB \) is part of a construction that involves several other equal-length segments, due to the properties of circles and compass constructions.

To identify the segments that are the same length as \( AB \):
- **\( AB \)** is a radius of the circle centered at \( A \) and the circle centered at \( B \).
- Therefore, any other radii of these circles should be of equal length to \( AB \).

### Segments of equal length to \( AB \):
- **\( BD \)**: \( BD \) is a radius of the circle centered at \( B \), so \( BD = AB \).
- **\( BC \)**: \( BC \) is also a radius of the circle centered at \( B \), so \( BC = AB \).
- **\( AD \)**: Since \( AD \) is a radius of the circle centered at \( A \), \( AD = AB \).

Thus, the segments that have the same length as \( AB \) are:
- \( BD \)
- \( BC \)
- \( AD \)

The correct selections should be:
- \( BD \)
- \( BC \)
- \( AD \)

Let me know if you'd like more details or further clarification! Here are some related questions you might want to explore:

1. Why are radii of the same circle always equal in length?
2. How can compass and straightedge tools create equal-length segments?
3. What properties of circles make all radii equal?
4. How would you prove that two segments are equal geometrically?
5. Can you identify any other equal-length segments in different geometric constructions?

**Tip:** Always remember that in geometric constructions using a compass, any segment that is the radius of the same or congruent circles will be equal in length!

Select all segments that have the same length as segment AB in the given geometric construction involving circles.

Learn how to identify segments that are equal in length using compass and straightedge constructions in a geometric problem. This example involves recognizing radii properties and using circle theorems to find segments equal to AB.

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