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>21s2,s1≦s2
B. for every triangle s1≧21s2,s1<s2
C. for every triangle s1>21s2,s1<s2
D. for every triangle s1≧21s2,s1≦s2
E. (E) neither (A) nor (B) nor (C) nor (D) applies to every triangle
Solution:
OA+OCOC+OBOB+OA2s1s1>AC>BC>AB>s2>21s2OB+OCOC+OAOA+OB2s1s1<AB+AC<BC+AB<AC+BC<2s2<s2