\(MA^2+MB^2=\overrightarrow{MA}.\overrightarrow{MA}+\overrightarrow{MB}.\overrightarrow{MB}=\left(\overrightarrow{MI}+\overrightarrow{IA}\right)\left(\overrightarrow{MI}+\overrightarrow{IA}\right)+\left(\overrightarrow{MI}+\overrightarrow{IB}\right)\left(\overrightarrow{MI}+\overrightarrow{IB}\right)\)
\(=\overrightarrow{MI}.\overrightarrow{MI}+2\overrightarrow{MI.}\overrightarrow{IA}+\overrightarrow{IA}.\overrightarrow{IA}+\overrightarrow{MI}.\overrightarrow{MI}+2\overrightarrow{MI.}\overrightarrow{IB}+\overrightarrow{IB}.\overrightarrow{IB}\)
\(=2MI^2+IA^2+IB^2+2\overrightarrow{MI}\left(\overrightarrow{IA}+\overrightarrow{IB}\right)\)
\(=2MI^2+IA^2+IB^2\)
\(=2MI^2+\left(\frac{a}{2}\right)^2+\left(\frac{a}{2}\right)^2=a^2\)
\(\Leftrightarrow MI^2=\frac{a^2}{4}\)
Suy ra \(M\)thuộc đường tròn tâm \(I\)bán kính \(\frac{a}{2}\).