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1966 AMC 12 Question 35

AMC12 · 1966 AMC 12

Question 35

Let $O$ be an interior point of triangle $ABC,$ and let $s_1=OA+OB+OC.$ If $s_2=AB+BC+CA,$ then:
  1. for every triangle $s_1\gt\dfrac12s_2,$ and $s_1\leq
    s_2$
  2. for every triangle $s_1\geq\dfrac12s_2,$ and $s_1\lt
    s_2$
  3. for every triangle $s_1\gt\dfrac12s_2,$ and
    $s_1\lt s_2$
  4. for every triangle $s_1\geq\dfrac12s_2,$ and $s_1\leq
    s_2$
  5. neither $(A)$ nor $(B)$ nor $(C)$ nor $(D)$ applies to
    every triangle