Inequalities? I prefer a geometric one!

Geometry Level 2

Let O , I O,I denote the circumcenter and the incenter of △ A B C \triangle ABC , respectively. A ′ A' is the point obtained by reflecting A A about O O (or O O is the midpoint of A A ′ AA' ). Define B ′ B' , C ′ C' analogously.

Which option can be filled in the blank below?

I A + I B + I C □ I A ′ + I B ′ + I C ′ IA+IB+IC\square IA'+IB'+IC'

≥ \geq = ≤ \leq None of the others.

X X by X X , 17, Taiwan

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