In triangle ABC the sides are AB = 7, AC = 9 and BC = 8. D is the midpoint of BC. What is the length of the median AD?

Apollonius' theorem states $A{B}^2+A{C}^2=2A{D}^2+2B{D}^2$, where $BD$ is half of $BC$. Here $BD=4$, so $49+81=2A{D}^2+2(16)$, giving $130=2A{D}^2+32$, then $A{D}^2=49$ and $AD=7$. Using the whole of $BC$ instead of half of it gives the wrong value √33.