[ Pythagorean Theorem (direct and inverse) ]

In rectangle $A B C D$, the lengths of segments $A B$ and $B D$ are 2 and $\sqrt{7}$, respectively. Point $M$ divides segment $C D$ in the ratio 1:2, counting from point $C$, and $K$ is the midpoint of $A D$. Which is greater: the length of $B K$ or the length of $A M$?
Answer

$A M>B K$.