This is a variant of the Polya's notorious "ALL Horses have the same color" paradox.
And the explanation is here - All horses are the same color (paradox) - Wikipedia, the free encyclopediaOriginally Posted by Wikipedia
Personally I think "same" is undefined for 1 element(you need two elements to say that).
And in your case "meeting at a point" needs 2 or more lines. And the explanation is that, for the statement to be >defined< you need two or more points. Hence the base case=1 is INVALID. Choose 2 and you will be in trouble