1966 AHSME Problems/Problem 35

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Problem

Let $O$ be an interior point of triangle $ABC$, and let $s_1=OA+OB+OC$. If $s_2=AB+BC+CA$, then

$\text{(A) for every triangle } s_2>2s_1,s_1 \le s_2 \\  \text{(B) for every triangle } s_2>2s_1,s_1 < s_2 \\  \text{(C) for every triangle } s_1> \tfrac{1}{2}s_2,s_1 < s_2 \\  \text{(D) for every triangle } s_2\ge 2s_1,s_1 \le s_2 \\  \text{(E) neither (A) nor (B) nor (C) nor (D) applies to every triangle}$

Solution

By the Triangle Inequality, we see that $s_1 > \frac12 s_2$, therefore $\fbox{C}$. -Dark_Lord

See also

1966 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 34
Followed by
Problem 36
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