[tex]\it d_1:\ 2x-y-2=0 \Rightarrow y=2x-2\ \ \ \ \ \ (1)\\ \\ d_2:\ x+3y-8=0 \Rightarrow y=\dfrac{1}{3}x+\dfrac{8}{3}\ \ \ \ \ (2)\\ \\ \\ Fie\ A(x,\ y)= d_1\cap d_2 \stackrel{(1),(2)}{\Longrightarrow}\ 2x-2=\dfrac{1}{3}x+\dfrac{8}{3}|_{\cdot3} \Rightarrow 6x-6=x+8 \Rightarrow\\ \\ \\ \Rightarrow 6x-x=8+6 \Rightarrow 5x=14|_{:5} \Rightarrow x=2,8\ \ \ \ \ (3)\\ \\ (1),\ (3) \Rightarrow y=2\cdot2,8-2 \Rightarrow y=5,6-2 \Rightarrow y=3,6[/tex]
[tex]\it Deci,\ d_1\cap d_2=A(2,8;\ \ 3,6)[/tex]
[tex]\it OA^2=(x_A-x_O)^2+(y_A-y_O)^2=2,8^2+3,6^2=7,84+12,96=20,8 \Rightarrow \\ \\ \Rightarrow OA=\sqrt{20,8}\approx4,56[/tex]
