The distance of the origin from the centroid of the triangle whose two sides have the equations x - 2y + 1 = 0 and 2x - y - 1 = 0 and whose orthocenter is $\left(\frac{7}{3},\frac{7}{3}\right)$ is 

$\begin{array}{r}\mathrm{AB}\equiv \mathrm{x}-2\mathrm{y}+1=0\\ \mathrm{AC}\equiv 2\mathrm{x}-\mathrm{y}-1=0\end{array}$
So A(1, 1)
Altitude from B is BO = (x-7/3) + 2(y -7/3) = 0 $\Rightarrow$ x + 2y - 7 = 0$\Rightarrow$B (3, 2)
Altitude from C is CO =2(x-7/3) + (y - 7/3) = 0 $\Rightarrow$2x + y - 7 = 0$\Rightarrow$C (2, 3)
Centroid of  $\mathrm{△}\mathrm{ABC}=\mathrm{E}(2,2)\mathrm{OE}=2\sqrt{2}$