Let O be the centre of the circle $\mathrm{x}^2+\mathrm{y}^2=\mathrm{r}^2$, where $\mathrm{r}>\frac{\sqrt{5}}{2}$. Suppose $P Q$ is a chord of this circle and the equation of the line passing through $P$ and $Q$ is $2 x+4 y=5$. If the centre of the circumcircle of the triangle $O P Q$ lies on the line $x+2 y=4$, then the value of $r$ is $\_\_\_\_$