I was one asked the answer to that with N=6. I noticed the pattern for N <= 5, but I suspected they were trying to trick me so I actually tried to determine it from scratch. (As for the “Obvious for low N, harder to prove for higher N” part, I used the heuristic that if no three of the lines met at one same point inside the circle, I had probably achieved the maximum. It worked.)

OTOH I was once asked "2, 3, 5, 7, what comes next?" and I immediately answered “that's the prime numbers, so it's 11”, but there was some other sequence they were thinking about (I can't remember which).