# 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

 1966 AHSME (Problems • Answer Key • Resources) Preceded byProblem 34 Followed byProblem 36 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions

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