Sure, here is the test case generator for the provided competitive programming problem:

```python
import random

def tcgen():
    # Define the range for N
    N = random.randint(1, 10**5)
    
    # Generate the list of strengths for 3N participants
    a = [random.randint(1, 10**9) for _ in range(3 * N)]
    
    return N, a

# Function to print the generated test case in the required format
def print_test_case():
    N, a = tcgen()
    print(N)
    print(" ".join(map(str, a)))

# Generate and print a test case
print_test_case()
```

### Explanation:
1. **Random Input Generation**:
   - The number of teams \( N \) is randomly generated within the range `[1, 10^5]`.
   - For \( 3N \) participants, their strengths \( a_i \) are generated randomly within the range `[1, 10^9]`.

2. **Output Formatting**:
   - The function `print_test_case()` prints the generated values in the specified format: first the integer \( N \), followed by the list of strengths.

By running the `print_test_case()` function, you can generate a test case in the required format for this competitive programming problem.