Find all triples $(a, b, c)$ of positive integers with $a+b+c=10$ such that there exist $a$ red, $b$ blue, and $c$ green points (all distinct) in the plane with the following properties:

- for each red point and each blue point, we consider the distance between these two points; the sum of all these distances is 37;
- for each green point and each red point, we consider the distance between these two points; the sum of all these distances is 30;
- for each blue point and each green point, we consider the distance between these two points; the sum of all these distances is 1;