$$\eqalign{
& G\,\,la\,\,trong\,\,tam\,\,\Delta ABC \cr
& \Rightarrow \overrightarrow {GA} + \overrightarrow {GB} + \overrightarrow {GC} = \overrightarrow 0 \cr
& \Leftrightarrow \overrightarrow {GI} + \overrightarrow {IA} + \overrightarrow {GI} + \overrightarrow {IB} + \overrightarrow {GI} + \overrightarrow {IC} = \overrightarrow 0 \cr
& \Leftrightarrow 3\overrightarrow {GI} + \left( {\overrightarrow {IA} + \overrightarrow {IB} + \overrightarrow {IC} } \right) = \overrightarrow 0 \cr
& \Leftrightarrow 3\overrightarrow {IG} = \overrightarrow {IA} + \overrightarrow {IB} + \overrightarrow {IC} \cr
& \Leftrightarrow \overrightarrow {IG} = {1 \over 3}\left( {\overrightarrow {IA} + \overrightarrow {IB} + \overrightarrow {IC} } \right) \cr} $$
