Problem: Let O be an interior point of triangle ABC and let s1​=OA+OB+OC. If s2​=AB+BC+CA, then
Answer Choices:
A. for every triangle s1​>21​s2​,s1​≦s2​
B. for every triangle s1​≧21​s2​,s1​<s2​
C. for every triangle s1​>21​s2​,s1​<s2​
D. for every triangle s1​≧21​s2​,s1​≦s2​
E. (E) neither (A) nor (B) nor (C) nor (D) applies to every triangle
Solution:
OA+OCOC+OBOB+OA2s1​s1​​>AC>BC>AB>s2​>21​s2​​OB+OCOC+OAOA+OB2s1​s1​​<AB+AC<BC+AB<AC+BC<2s2​<s2​​​