Let $P=(S,L)$ be a projective plane of order $n$. Let $K$ be a nonempty subset of $S$ with the property that no three points belonging to $K$ are collinear. Prove that $|K|$ is less than or equal to $n+2$.
I began by staying that since $P$ is of order $n$, there are exactly $n^2+n+1$ points in $S$ and since $K$ has the stipulation that no three points are collinear, the points in $K$ must be at least on two lines. Now here is where I'm stuck. I don't know how to go from there to less than or equal to $n+2$. Any help would be appreciated.