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 PQ is a chord of this circle and  the equation of the line passing through P and Q is $2x+4y=5$. If the centre of the circumcircle of the triangle  OPQ lies on the line $x+2y=4 ,$then the value of $r$ is