MathDB
Which is True?

Source: 1966 AHSME #35

August 31, 2011
AMC

Problem Statement

Let OO be an interior point of triangle ABCABC, and let s1=OA+OB+OCs_1=OA+OB+OC. If s2=AB+AC+CAs_2=AB+AC+CA, then
(A) for every triangle s2>2s1,s1≤s2(B) for every triangle s2≥2s1,s1<s2(C) for every triangle s1>12s2,s1<s2(D) for every triangle s2≥2s1,s1≤s2(E) neither (A) nor (B) nor (C) nor (D) applies to every triangle\text{(A)}\ \text{for every triangle }s_2>2s_1,s_1\le s_2\qquad\\ \text{(B)}\ \text{for every triangle } s_2\ge2s_1,s_1<s_2\qquad\\ \text{(C)}\ \text{for every triangle } s_1>\tfrac{1}{2}s_2,s_1<s_2\qquad\\ \text{(D)}\ \text{for every triangle }s_2\ge2s_1,s_1\le s_2\qquad\\ \text{(E)}\ \text{neither (A) nor (B) nor (C) nor (D) applies to every triangle}
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