$$\eqalign{
& \left| {\overrightarrow {MA} + \overrightarrow {MB} - \overrightarrow {MC} } \right| = \left| {\overrightarrow {AB} - \overrightarrow {CB} } \right| \cr
& \Leftrightarrow \left| {\overrightarrow {MA} + \overrightarrow {MB} - \overrightarrow {MC} } \right| = \left| {\overrightarrow {AC} } \right| = AC \cr
& Goi\,\,I\,\,la\,\,diem\,\,thoa\,\,man\,\,\overrightarrow {IA} + \overrightarrow {IB} - \overrightarrow {IC} = \overrightarrow 0 \,\,ta\,\,co: \cr
& \left| {\overrightarrow {MI} + \overrightarrow {IA} + \overrightarrow {MI} + \overrightarrow {IB} - \overrightarrow {MI} - \overrightarrow {IC} } \right| = AC \cr
& \Leftrightarrow \left| {\overrightarrow {MI} + \left( {\overrightarrow {IA} + \overrightarrow {IB} - \overrightarrow {IC} } \right)} \right| = AC \cr
& \Leftrightarrow \left| {\overrightarrow {MI} } \right| = AC \Leftrightarrow MI = AC. \cr
& Do\,\,\Delta ABC\,\,co\,\,dinh \Rightarrow I\,\,co\,\,dinh\,\,va\,\,AC\,\,khong\,\,doi. \cr
& \Rightarrow Tap\,\,hop\,\,diem\,\,M\,\,la\,\,duong\,\,tron\,\,tam\,\,I,\,\,ban\,\,kinh\,\,AC. \cr} $$
