Let $O$ be an interior point of triangle $ABC$, and let $s_1=OA+OB+OC$. If $s_2=AB+BC+CA$, then
$\text{(A) for every triangle } s_2>2s_1,s_1 \le s_2 \\  \text{(B) for every triangle } s_2>2s_1,s_1  \tfrac{1}{2}s_2,s_1 < s_2 \\  \text{(D) for every triangle } s_2\ge 2s_1,s_1 \le s_2 \\  \text{(E) neither (A) nor (B) nor (C) nor (D) applies to every triangle}$
By the Triangle Inequality, we see that $s_1 > \frac12 s_2$, therefore $\fbox{C}$. -Dark_Lord