https://file.aiquickdraw.com/mathbot/file/17255539821680uly4dx1.jpg

The image contains a diagram of two identical circles intersecting each other, with centers \( A \) and \( B \) respectively. Points \( A, B, C, \) and \( D \) lie on the circumference of the circles. The task is to find the degree of the angle subtended by chord \( CD \) at the center of circle \( B \). 

### Analysis

1. **Understanding the Diagram:**
   - The two circles intersect at points \( C \) and \( D \).
   - Center \( A \) belongs to one circle, and center \( B \) belongs to the other.
   - The line segment \( CD \) passes through the points where the circles intersect.
   - The question asks for the angle subtended by chord \( CD \) at the center of circle \( B \).

2. **Key Observations:**
   - Since the circles are identical, they have the same radius, say \( r \).
   - The line segment \( AB \) connects the centers of the two circles.
   - \( CD \) is a common chord for both circles and is perpendicular to \( AB \).

3. **Geometric Properties:**
   - Since \( CD \) is a common chord and the circles are identical, \( AB \) bisects \( CD \) at right angles.
   - Triangle \( BCD \) is isosceles with \( BC = BD = r \) (radius of circle with center \( B \)).

4. **Finding the Angle \( \angle CBD \):**
   - In the isosceles triangle \( BCD \), \( \angle CBD = 90^\circ \) because the line \( AB \) is perpendicular to the chord \( CD \).

Thus, the degree of the angle subtended by chord \( CD \) at the center of circle \( B \) is **90 degrees**.

### Would you like more details or explanations?

#### Related Questions:
1. How do you calculate the length of a chord in a circle?
2. How can we prove that the angle subtended by a diameter of a circle is 90 degrees?
3. What is the relationship between the radius of a circle and its chords?
4. How do you find the area of a segment of a circle?
5. How do intersecting chords within a circle relate to each other?

#### Tip:
When solving problems involving intersecting circles, look for symmetry and consider the properties of common chords and perpendicular bisectors.

The diagram shows two identical circles with overlapping areas. Points A, B, C, and D are all on the circumference of CD. Name the degree of the angle that the line CD subtends from the center of circle B.

This geometry problem involves two identical intersecting circles. The task is to find the angle subtended by the chord CD at the center of circle B. Learn about circle theorems, isosceles triangles, and chord properties. Suitable for students in Grades 9-11.

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