a) \(\left( {\Delta '} \right)//\left( \Delta  \right) \Rightarrow {\overrightarrow a _{\Delta '}} = \left( {2;1} \right)\)

Phương trình \((\Delta) '\) qua I(1;2) và \({\overrightarrow a _{\Delta '}} = \left( {2;1} \right)\): \(2(x-1)+1(y-2)=0 \Leftrightarrow 2x + y - 4 = 0\)

b) \(\cos \widehat {\left( {OM;IM} \right)} = \frac{{\left| {x\left( {x - 1} \right) + y\left( {y - 1} \right)} \right|}}{{\sqrt {{x^2} + {y^2}} .\sqrt {{{\left( {x - 1} \right)}^2} + {{\left( {y - 1} \right)}^2}} }}\)

\( = \frac{{4 - \left( {x + y} \right)}}{{2\sqrt 2 .\sqrt {3 - \left( {x + y} \right)} }} = \frac{1}{{\sqrt 2 }}\left[ {\frac{{1 + 3 - \left( {x + y} \right)}}{{2\sqrt {3 - \left( {x + y} \right)} }}} \right] \ge \frac{1}{{\sqrt 2 }}\)

Ycbt \( \Leftrightarrow \) Dấu bằng xảy ra \( \Leftrightarrow \left\{ \begin{array}{l}
{x^2} + {y^2} = 4\\
1 = 3 - \left( {x + y} \right)
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 2\\
y = 0
\end{array} \right. \vee \left\{ \begin{array}{l}
x = 0\\
y = 2
\end{array} \right.\)