This may not be suitable for several reasons. But anyway, I like Exercise 4.18.3 from A. Beauvilles "Complex Algebraic Surfaces".

Let $S$ be an irreducible surface in $\mathbb{CP}^n$ of degree $d \leq n-2$. Show that $S$ is contained in a hyperplane.

The idea of the solution is definitely used elsewhere in algebraic geometry but outside of it maybe not.