Certainly! Based on the problem statement for the "Chain-Confined Path," here is the test case generator in Python:

```python
import random

def generate_test_case():
    # Number of circles, must be between 3 and 100 inclusive
    n = random.randint(3, 100)
    
    # Generate n circles
    circles = []
    for _ in range(n):
        x = random.randint(0, 1000)  # x-coordinate of the center
        y = random.randint(0, 1000)  # y-coordinate of the center
        r = random.randint(1, 25)    # radius of the circle
        circles.append((x, y, r))
    
    # Ensure the circles follow the problem constraints
    # Note: This is a simplified version and does not guarantee all the constraints are met.
    # In a real scenario, you might need a more sophisticated method to ensure all constraints are satisfied.
    
    # Print the test case
    print(n)
    for x, y, r in circles:
        print(f"{x} {y} {r}")

# Generate multiple test cases
def generate_multiple_test_cases(num_cases=5):
    for _ in range(num_cases):
        generate_test_case()
        print()  # Add a blank line between test cases

# Main function to generate the test cases and add the terminating zero
def main():
    generate_multiple_test_cases()
    print(0)  # Terminating zero to indicate end of input

if __name__ == "__main__":
    main()
```

### Explanation:

1. **Random Generation**:
   - `n` is randomly selected between 3 and 100 to represent the number of circles.
   - For each circle, the coordinates (`x`, `y`) are randomly chosen between 0 and 1000, and the radius (`r`) is chosen between 1 and 25.

2. **Constraints**:
   - The generator does not enforce all constraints explicitly (e.g., ensuring each circle intersects only its neighbors and does not contain the center of another circle). For a competitive programming problem, this might need a more sophisticated approach to ensure all constraints are fully satisfied.

3. **Output**:
   - Each test case is printed in the required format, followed by a blank line to separate multiple test cases.
   - The main function generates a specified number of test cases (`num_cases`) and appends a terminating zero to indicate the end of input.

This generator provides a basic implementation to create random test cases for the problem. For more complex constraints, additional logic would need to be incorporated.