\(\begin{array}{l}
A\left( {5;\,\,1} \right),\,\,\,B\left( { - 1;\,\,5} \right)\\
\Rightarrow \left\{ \begin{array}{l}
O{A^2} = {\left( {5 - 0} \right)^2} + {\left( {1 - 0} \right)^2} = 26\\
O{B^2} = {\left( { - 1 - 0} \right)^2} + {\left( {5 - 0} \right)^2} = 26\\
A{B^2} = {\left( { - 1 - 5} \right)^2} + {\left( {5 - 1} \right)^2} = 52
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
O{A^2} = O{B^2} = 26\\
A{B^2} = O{A^2} + O{B^2}
\end{array} \right.\\
\Rightarrow \Delta AOB\,\,\,vuong\,\,can\,\,tai\,\,O.\\
Chu\,\,vi\,\,\Delta AOB\,\,la:\,\,\,OA + OB + OC = \sqrt {26} + \sqrt {26} + \sqrt {52} = 2\sqrt {26} + 2\sqrt {13} .\\
Dien\,\,tich\,\,\Delta AOB\,\,\,la:\,\,\,\frac{1}{2}OA.OB = \frac{1}{2}{\left( {\sqrt {26} } \right)^2} = 13.
\end{array}\)
