Hey!

I have this problem: In triangle $\displaystyle ABC$, $\displaystyle |AC|$ is $\displaystyle 9$, $\displaystyle |BC|$ is $\displaystyle 7$. Point $\displaystyle M$ is the midpoint of $\displaystyle |AB|$, and $\displaystyle |CM|$ is also $\displaystyle 7$. What is the length of $\displaystyle |AB|$

The only way to solve the problem, that I can think of is using the cosine rule, but it is said that the problem could be solved without using trigonometry. Can anyone give me an idea how?