Sure, I can help you with that. Below is a test case generator for the problem statement involving the Extended Euclid Algorithm.

```python
import random

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def tcgen():
    # Generating two positive integers a and b
    a = random.randint(1, 10**9)
    b = random.randint(1, 10**9)
    
    # Ensuring a <= b for sample output consistency
    if a > b:
        a, b = b, a

    return f"{a} {b}"

# Example usage
for _ in range(5):  # Generate 5 test cases
    print(tcgen())
```

### Explanation:
1. **Importing random module**: To generate random integers.
2. **GCD Function**: This is a helper function to compute the greatest common divisor. It is not directly used in the test case generation but can be useful for debugging or verifying test cases.
3. **tcgen Function**: This is the main test case generator.
    - It generates two random integers `a` and `b` in the range `[1, 10^9]`.
    - It ensures that `a` is less than or equal to `b` for consistency in sample outputs.
    - It returns the test case in the string format as required by the problem statement.

### Example Usage:
To generate multiple test cases, you can call `tcgen()` multiple times, as shown in the example usage. You can change the number of iterations based on how many test cases you need. 

This generator ensures you have diverse test cases while respecting the given constraints of the problem.