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Given that \( A \), \( B \), and \( C \) are the centers of the three circles, we can analyze which segments are congruent to \( AB \).

Since \( A \), \( B \), and \( C \) are the centers of the circles, each of the segments \( AB \), \( BC \), and \( CA \) are radii of their respective circles, which means:

- \( AB \) is congruent to \( BC \) and \( CA \) since all three are radii of circles centered at \( A \), \( B \), and \( C \).

Now, let's evaluate the given segments:

1. **BF**: Not congruent to \( AB \); \( BF \) is not a radius.
2. **HF**: Not congruent to \( AB \); \( HF \) is an external chord.
3. **CE**: Congruent to \( AB \) since it represents a radius of the circle centered at \( C \).
4. **HA**: Congruent to \( AB \) because it is a radius of the circle centered at \( A \).
5. **BD**: Congruent to \( AB \) since it is a radius of the circle centered at \( B \).
6. **CD**: Congruent to \( AB \) since it is a radius of the circle centered at \( C \).

Thus, the segments that are congruent to \( AB \) are: **CE, HA, BD,** and **CD**.

Would you like further details or have any questions?

**Related Questions:**
1. What is the relationship between chords and radii in a circle?
2. How can you determine if two line segments are congruent?
3. What geometric properties define the center of a circle?
4. How are congruent segments used in geometric proofs?
5. What are the different types of segments found in a circle?

**Tip:** When identifying congruent segments in geometric figures involving circles, always look for radii and symmetry patterns!

Select all the segments that are congruent to AB. A, B, and C are the centers of the three circles in the diagram provided.

Analyze a geometric diagram with three intersecting circles. Learn how to identify which segments are congruent to AB, based on the principles of congruence and circle radii. Suitable for students in Grades 9-11.

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