Find the combination that gives the minimum sum of squares

[tandemuse]

I have a number of vectors A,B,C,...etc as a pair of numbers such as below:

		x​	y​
1​	A​	2​	4​
2​	B​	5​	6​
3​	C​	3​	9​

I want to list or at least find the combination that produces the minimum x^2 + y^2, by taking combinations by 2 or 3 vectors. I've tried solver unsuccessfully.....

Thank you.

 

[tandemuse]

* Important clarification: for example a combination by 2, AB gives the sum A+B so we have (A+B)=(7,10) of which 7^2+10^2 is a possible sum of squares