I'm studying for my exam in Algebraic Geometry next week, and stumbled upon this problem:
Let $X$ be a variety, and $P \in X$ a nonsingular point. Suppose $H$ is some hyperplane, containing $P$ but not containing $X$. Then: $$ \deg (X\cap H) = \deg(X) \deg(H) (= \deg(X)).$$ Any hints are appreciated. For me, the biggest problem is that I don't understand why we want $P$ to be non-singular.