8. $A B C D$ is a square with sides $8 \mathrm{~cm} . M$ is a point on $C B$ such that $C M=2 \mathrm{~cm}$. If $N$ is a variable point on the diagonal $D B$, find the least value of $C N+M N$.
(A) 8
(B) $6 \sqrt{2}$
(C) 10
(D) $8 \sqrt{2}$
(E) 12
8. Answer: (C)
Join $A$ to $N$. By symmetry, $A N+N M=M N+C N$, and the least value occurs when ANM is a straight line. Thus the least value is
$$
\sqrt{A B^{2}+B M^{2}}=\sqrt{8^{2}+6^{2}}=10 .
$$